To solve the equation \(0 - 4\frac{3}{8}\), we start by recognizing that subtracting a number is the same as adding its negative. Therefore, we can rewrite the expression as:
\[ 0 - 4\frac{3}{8} = -4\frac{3}{8} \]
Next, we can convert \(4\frac{3}{8}\) to an improper fraction:
\[ 4\frac{3}{8} = \frac{4 \times 8 + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8} \]
Thus, we have:
\[ 0 - 4\frac{3}{8} = -\frac{35}{8} \]
Therefore, the answer is:
\[ -\frac{35}{8} \]
