To solve the equation \( 2^{(x+2)} = 4^2 \), we can first express \( 4^2 \) in terms of base 2.
We know that:
\[ 4 = 2^2 \]
Thus,
\[ 4^2 = (2^2)^2 = 2^{2 \cdot 2} = 2^4 \]
Now we can rewrite 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 can solve for \( x \):
\[ x = 4 - 2 \] \[ x = 2 \]
Therefore, the missing value is \( \boxed{2} \).