To solve the equation \( x - \frac{9}{4} = -\frac{3}{8} \), we can isolate \( x \) by adding \(\frac{9}{4}\) to both sides of the equation.
\[ x = -\frac{3}{8} + \frac{9}{4} \]
Next, we need to have a common denominator to combine the fractions. The common denominator for \( 8 \) and \( 4 \) is \( 8 \). We can convert \(\frac{9}{4}\) to have a denominator of \( 8 \):
\[ \frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8} \]
Now, substitute this back into the equation:
\[ x = -\frac{3}{8} + \frac{18}{8} \]
Combine the fractions:
\[ x = \frac{-3 + 18}{8} = \frac{15}{8} \]
Thus, the solution to the equation is:
\[ \boxed{\frac{15}{8}} \]