To solve the equation \( x - 8 = -12 \), we need to isolate \( x \). We can do this by adding 8 to both sides of the equation:
\[ x - 8 + 8 = -12 + 8 \]
This simplifies to:
\[ x = -4 \]
Thus, the integer that makes the addition sentence true is \( \boxed{-4} \).