Let's simplify the given equation step by step:
\[ -4w - 8 - 11w = -15w - 7 \]
First, combine the terms on the left side:
\[ (-4w - 11w) - 8 = -15w - 7 \]
This simplifies to:
\[ -15w - 8 = -15w - 7 \]
Next, add \(15w\) to both sides of the equation:
\[ -8 = -7 \]
This statement is not true. The equation results in a contradiction, which implies that there are no values of \(w\) that satisfy the equation.
Therefore, the equation has \(\boxed{0}\) solutions.