To solve the equation, we can rewrite it as:

(-2/3)^(x-3) = (2/3)^4

Now, we can rewrite both sides of the equation using positive exponents:

(3/2)^(3-x) = (3/2)^4

Since the bases are the same, we can equate the exponents:

3 - x = 4

Solving for x, we subtract 3 from both sides:

-x = 1

Multiplying both sides by -1, we get:

x = -1

Therefore, the solution to the equation is x = -1.