To solve the equation \(-\frac{2}{x} = \frac{4}{7}\), we can start by cross-multiplying to eliminate the fractions.
Cross-multiplying gives us:
\[ -2 \cdot 7 = 4 \cdot x \]
This simplifies to:
\[ -14 = 4x \]
Now, to solve for \(x\), divide both sides by 4:
\[ x = \frac{-14}{4} \]
Simplifying \(\frac{-14}{4}\) gives:
\[ x = \frac{-7}{2} \]
Thus, the solution is:
\[ \boxed{-\frac{7}{2}} \]