There are ambiguities here. Let's first assume that the question is log3(x+3)*log3(x-3)=4. This is the most difficult to solve. In this case, x=3.8816 approx. This solution required trial and error. It wasn't possible to solve using conventional methods because x is included in an exponent: (3(x+3))^(3(x-3))=e^4 (assuming natural logs).
Let's now assume that the question is log3(x+3)-log3(x-3)=4. This is the same as log[3(x+3)/(3(x-3))]=4=log[(x+3)/(x-3)]. Raise both sides as powers of e (assuming natural logs): (x+3)/(x-3)=e^4=54.59815. So x+3=54.59815x-163.79445 and 53.59815x=166.79445, so x=3.112 approx. If logs to base 10, x=10001/3333=3.0006.
Finally, assume the question is log3(x+3)+log3(x-3)=4, then log[9(x^2-9)]=e^4. So x^2-9=(e^4)/9=6.06646. Therefore x^2=15.06646 and x=3.8816. If logs to base 10, x=33.468.