After cutting the wire into 8 equal pieces:

Resistance of each piece:

Each piece has a resistance $R' = \frac{R}{8}$.

Parallel Combination in Each Set:

Each set consists of 4 pieces connected in parallel:

Resistance of each set:

$ R'' = \frac{R'}{4} = \frac{R}{32} $

Connecting the Sets in Series:

With both sets connected in series, the equivalent resistance is calculated as:

$ R_{\text{eq}} = R'' + R'' = 2 \times \frac{R}{32} = \frac{R}{16} $

Thus, the net effective resistance of the combination is $\frac{R}{16}$.