How can you tell what is the net direction of current flow when there are two opposing sources?
Redraw Schematics First
Often, it helps a great deal to redraw a schematic. Not always. But sometimes the manual process of it helps you find an insight or two or, at least, develops a feel for things over time as you do it again and again.
Below, I started out by following a rule in the appendix below: don't bus power around:



simulate this circuit &ndash; Schematic created using CircuitLab
I also noticed that your two current sources can be reduced, as shown above. If you want to see how, just replace the \$3\:\text{A}\$ current source with two of them, in series. (That's not a difference in anything.) Once you've done that, you can &quot;cut&quot; the link between them (they have infinite impedance, anyway) and then notice that there's a \$5\:\text{A}\$ source into a node and a \$3\:\text{A}\$ source out of the node, which is the same as just a \$2\:\text{A}\$ source into that node. So the above schematic summarizes that, as well.
Nodal Analysis
Nodal analysis is just KCL in action. The following equations are developed by examining first the outflowing currents (placed on the left) and the inflowing currents (placed on the right.) According to KCL, these two currents must be equal:
$$\begin{align*}
  \begin{array}{c}
  {V_1}\vphantom{\frac{V_1}{R_1}}\\\\{V_2}\vphantom{\frac{V_1}{R_1}}\\\\{V_3}\vphantom{\frac{V_1}{R_1}}
  \end{array}
&amp;&amp;
\overbrace{
 \begin{array}{r}
      \frac{V_1}{R_4} + \frac{V_1}{R_5} + \frac{V_1}{R_6}\\\\
      \frac{V_2}{R_2} + \frac{V_2}{R_3} + \frac{V_2}{R_4}\\\\
      \frac{V_3}{R_1} + \frac{V_3}{R_2} + \frac{V_3}{R_6}
 \end{array}
  }^{\text{outflowing currents}}
&amp;
  \begin{array}{c}
  &amp;\quad{=}\vphantom{\frac{V_1}{R_1}}\\\\&amp;\quad{=}\vphantom{\frac{V_1}{R_1}}\\\\&amp;\quad{=}\vphantom{\frac{V_1}{R_1}}
  \end{array}
&amp;
\overbrace{
 \begin{array}{l}
      \frac{V_2}{R_4} + \frac{V_3}{R_6} + 2\:\text{A}\\\\
      \frac{V_3}{R_2} + \frac{V_1}{R_4}\\\\
      \frac{12\:\text{V}}{R_1} + \frac{V_2}{R_2} + \frac{V_1}{R_6} + 3\:\text{A}
 \end{array}
  }^{\text{inflowing currents}}
\end{align*}$$
You can use the above as three equations in three unknowns and solve for all three node voltages using linear algebra methods. Cramer's rule is sometimes used when you are stuck doing these things by hand. So look that up. Otherwise, use free tools such as sympy for symbolic algebra and sage for numerical algebra.
Summary
No, there's no magic wand you can wave in order to decide if the voltage source is overwhelmed and is absorbing energy over time, or expending it. You just need to push though the details and see.
Appendix

One of the better ways to try and understand a circuit that at first
appears to be confusing is to redraw it. There are some rules you can
follow that will help get a leg-up on learning that process. But there
are also some added personal skills that gradually develop over time,
too.
I first learned these rules in 1980, taking a Tektronix class that was
offered only to its employees. This class was meant to teach
electronics drafting to people who were not electronics engineers, but
instead would be trained sufficiently to help draft schematics for
their manuals.
The nice thing about the rules is that you don't have to be an expert
to follow them. And that if you follow them, even blindly almost, that
the resulting schematics really are easier to figure out.
The rules are:

Arrange the schematic so that conventional current appears to flow from the top towards the bottom of the schematic sheet. I like to
imagine this as a kind of curtain (if you prefer a more static
concept) or waterfall (if you prefer a more dynamic concept) of
charges moving from the top edge down to the bottom edge. This is a
kind of flow of energy that doesn't do any useful work by itself, but
provides the environment for useful work to get done.
Arrange the schematic so that signals of interest flow from the left side of the schematic to the right side. Inputs will then
generally be on the left, outputs generally will be on the right.
Do not &quot;bus&quot; power around. In short, if a lead of a component goes to ground or some other voltage rail, do not use a wire to connect it
to other component leads that also go to the same rail/ground.
Instead, simply show a node name like &quot;Vcc&quot; and stop. Busing power
around on a schematic is almost guaranteed to make the schematic less
understandable, not more. (There are times when professionals need to
communicate something unique about a voltage rail bus to other
professionals. So there are exceptions at times to this rule. But when
trying to understand a confusing schematic, the situation isn't that
one and such an argument &quot;by professionals, to professionals&quot; still
fails here. So just don't do it.) This one takes a moment to grasp
fully. There is a strong tendency to want to show all of the wires
that are involved in soldering up a circuit. Resist that tendency. The
idea here is that wires needed to make a circuit can be distracting.
And while they may be needed to make the circuit work, they do NOT
help you understand the circuit. In fact, they do the exact opposite.
So remove such wires and just show connections to the rails and stop.
Try to organize the schematic around cohesion. It is almost always possible to &quot;tease apart&quot; a schematic so that there are
knots of components that are tightly connected, each to another, separated then by only a few wires going to other knots. If you
can find these, emphasize them by isolating the knots and focusing
on drawing each one in some meaningful way, first. Don't even think
about the whole schematic. Just focus on getting each cohesive section
&quot;looking right&quot; by itself. Then add in the spare wiring or few
components separating these &quot;natural divisions&quot; in the schematic. This
will often tend to almost magically find distinct functions that are
easier to understand, which then &quot;communicate&quot; with each other via
relatively easier to understand connections between them.

The above rules aren't hard and fast. But if you struggle to follow them,
you'll find that it does help a lot.
I also tell a bit of a tale and provide some examples of successful drafting
of schematics here.