Which of the following is an equivalent fraction of $\frac{4}{7}$ with numerator 92?

The given fraction is $\frac{4}{7}$.

We know, 4 × 23 = 92. 

This means we need to multiply both the numerator and denominator by 23 to get an equivalent fraction,

Thus, $\frac{4}{7}$ = $\frac{4\times 23}{7\times 23}=\frac{92}{161}$

Hence, the equivalent fraction of $\frac{4}{7}$ with numerator 92 is $\frac{92}{161}$.