imc

Since there are $n^2$ little faces on each face of the big wooden cube, there are $6n^2$ little faces painted red. Since each unit cube has $6$ faces, there are $6n^3$ little faces total. Since one-fourth of the little faces are painted red, $\frac{6n^2}{6n^3}=\frac{1}{4}$ $\frac{1}{n}=\frac{1}{4}$ $n=\boxed{4}$