Convert the logarithmic equation into exponential form. The statement log_4(x + 6) = 4 means x + 6 = 4^4. Now calculate 4^4 = 256, so x + 6 = 256. Subtract 6 from both sides: x = 256 - 6 = 250. Finally, check the domain: x + 6 must be positive, and 250 + 6 = 256 > 0, so the answer is valid.