2^n = 4^(n - 3)

2^n = 4^(n - 3)

2^n = (2^2)^(n - 3)
(2^2)^(n - 3) = 2^2(n - 3)
2^n= 2^2(n - 3)

Comparing exponents, we see that:
n = 2(n - 3)
n = 2n - 6

Subtract n from each side:
n - n = 2n - n - 6
0 = n - 6
n = 6