Answer
The diameter is $\frac{3}{16}$ inches.
Work Step by Step
$\frac{15}{16} - \frac{3}{8} - \frac{3}{8}$
Visual inspection shows the LCM is 16. Express as like fractions and subtract.
$\frac{15}{16} - \frac{3}{8} - \frac{3}{8}$ = $\frac{15}{16} - \frac{6}{16} - \frac{6}{16}$ = $\frac{3}{16}$