For maximum power, R(L) should be equal to R(TH) in Thevinin's Equivalent Circuit. So am I right to say that all I need to do is find R(TH) and I'll be done? I believe I have a conceptual error here as I am unable to find the answer as displayed above.

What I did was to remove all power sources from the circuit first, so then Vx would be zero since the dependent source is zero. My idea was that since Vx through the dependent source is zero, then the object that it's dependent on would also have a zero Vx. (ie. the p.d. across the 4 ohm resistor which has the Vx on it is zero and hence removed). Doing so would give me a 8/3 ohm resistance for R(TH) which is certainly not the answer.

My guess is that the dependent source plays a part in R(TH), but I was struggling over the question for a while unable to get anything resembling the 3 ohm answer above. So, any help here would be greatly appreciated. Thanks!