Before I call out my professor for this. I want to confirm, this is incorrect right?

No, that's correct.

Here's the proof:
y = a^x
ln y = ln (a^x)
ln y = x ln a
d/dx (ln y) = d/dx (x ln a)
y' / y = ln a
y' = (ln a) y
y' = (ln a) (a^x)

In this case, y = 2^(3x) = (2^3)^x = 8^x.
So y' = (ln 8) (8^x)

　
Thank goodness you came here to confirm.
It will save you some embarrassment.
The above is quite correct.

3 ln 2 = ln(2^3) = ln 8
2^(3x) = (2^3)^x = 8^x

You can also use WolframAlpha to check:
http://www.wolframalpha.com/input/?i=d%2Fdx+(2%5E(3x))