To find the distance between the points \( N(-7, -11) \) and \( P(-7, -4) \), we can use the distance formula. However, since both points have the same x-coordinate (\(-7\)), we can simply find the distance by calculating the difference in the y-coordinates.
The y-coordinates for the points are:
- For point \( N \): \( y_N = -11 \)
- For point \( P \): \( y_P = -4 \)
The distance \( d \) between the points can be calculated as follows:
\[ d = |y_P - y_N| = |-4 - (-11)| = |-4 + 11| = |7| = 7 \]
Therefore, the distance between the points \( N \) and \( P \) is \( \boxed{7} \).