To find the y-intercept of the line given by the equation \( y = -\frac{8}{5}x - 4 \), we need to evaluate the equation when \( x = 0 \).
Substituting \( x = 0 \):
\[ y = -\frac{8}{5}(0) - 4 \]
This simplifies to:
\[ y = -4 \]
Thus, the y-intercept of the line is:
\[ \boxed{-4} \]