Mesh Analysis with voltage and current source
Bad news is that your \$I_3\$ equation is wrong, good one is you shouldn't write it at all.

Writing \$14\,I_3-4\,I_2=0\$ your are just considering voltage across current generator \$I_3\$ naugh.
But this is not (generally) true, this voltage will be some unknown value. 

What you can do is just skip it so far. You only have two unknowns \$I_1\$ and \$I_2\$, then you only have to solve their system, substituting known -6A whenever you find a reference to \$I_3\$.

So, your \$I_2\$ equation will become:  

\$-2\,I_1+9\,I_2-4\,I_3=0 \quad\Rightarrow\quad -2\,I_1+9\,I_2-4\times(-6)=0\$

which can be used to build this 2x2 system
$$
\left\{\begin{align}
2\,I_1-2\,I_2&amp;=10 \\
-2\,I_1+9\,I_2&amp;=-24
\end{align}\right.
$$


  Generally a circuit with M meshes and C current generator branches is solved with an M-C unknowns system. E.g. 3-1=2 in your sketch.


Afterwards, once solved the above, you have all the three currents, the circuit is solved. If you happen to need voltage across current generator  you just use Ohm's law.