How to calculate power from current and voltage, both of which are sinusoidal waveforms represented by phasors
The way to calculate power with two V and I rms phasors is

\$S = V \cdot I^{*}\$

S is apparent power, which is composed of the following:

\$S = P + jQ\$

Q is reactive power, and P is active power, which is what you are looking for.

So, let's apply this to your case:

\$S = (4.35 + j8.2) \cdot (9.4 - j5.5) = 87.4 + j52.33 \$

Now, this doesn't match your expected result, but there is one missing piece of information, you didn't mention if the phasors are rms phasors or peak phasors. It seems like they are peak phasors, so then we can transform through this equation (which only applies for sinusoidal signals):

\$V_{rms} = \frac{V_{peak}}{\sqrt{2}}\$

And then this gives

\$S = \frac{ (4.35 + j8.2) }{\sqrt{2}} \cdot \frac{(9.4 - j5.5)}{\sqrt{2}} = 43.7 + j26.16 \$

And, the real part of that result is the real power P, so

\$ P = 43.7 \$