To solve the equation
\[ \frac{3}{8} + \frac{2}{x} = \frac{1}{4}, \]
we can start by isolating the term involving \(x\). First, we subtract \(\frac{3}{8}\) from both sides:
\[ \frac{2}{x} = \frac{1}{4} - \frac{3}{8}. \]
To perform this subtraction, we need a common denominator. The least common denominator of 4 and 8 is 8. We can rewrite \(\frac{1}{4}\) as \(\frac{2}{8}\):
\[ \frac{2}{x} = \frac{2}{8} - \frac{3}{8} = \frac{2 - 3}{8} = \frac{-1}{8}. \]
Now we have
\[ \frac{2}{x} = \frac{-1}{8}. \]
Next, we cross-multiply to eliminate the fractions:
\[ 2 \cdot 8 = -1 \cdot x \implies 16 = -x. \]
This gives us
\[ x = -16. \]
Thus, the solution to the equation is
\[ \boxed{-16}. \]