Answer
$$\frac{1}{2}$$
Work Step by Step
We simplify the expression using the fact that dividing by a fraction is the same as multiplying by the inverse:
$$ \frac{3}{8}\times \frac{4}{3}\\ \frac{3\times \:4}{8\times \:3}\\ \frac{4}{8}\\ \frac{1}{2}$$