Answer: C

To solve this problem, you'll need to be able to set the exponents equal to each other. You can't do that until the bases are equal. Since 9 = 3^2, you can rewrite the left side as:
(3^2)^(x+3)
= 3^(2x + 6)

Now that both sides have a base of 3, the exponents must be equal:
2x + 6 = 4x - 1
7 = 2x
x = 7/2, choice (C).