To solve the equation \( 2^{(x+2)} = 4^2 \), we first simplify the right side of the equation.
We know that \( 4 \) can be expressed as \( 2^2 \). Therefore, \( 4^2 \) can be rewritten as:
\[ 4^2 = (2^2)^2 = 2^{2 \cdot 2} = 2^4 \]
Now, we can replace \( 4^2 \) in the original equation:
\[ 2^{(x + 2)} = 2^4 \]
Since the bases are the same, we can set the exponents equal to each other:
\[ x + 2 = 4 \]
Now, we solve for \( x \) by subtracting \( 2 \) from both sides:
\[ x = 4 - 2 \]
\[ x = 2 \]
Thus, the solution is:
\[ \boxed{2} \]