To solve the equation \( -16 - x = -22 \), we can isolate \( x \).
First, we can add \( 16 \) to both sides of the equation:
\[ -16 - x + 16 = -22 + 16 \]
This simplifies to:
\[ -x = -6 \]
Next, we multiply both sides by \( -1 \):
\[ x = 6 \]
So, the integer that makes the subtraction sentence true is \( \boxed{6} \).