The rod and the flagpole cast shadows at the same time, so they form similar triangles. Set up a proportion:

$\frac{\text{Rod height}}{\text{Rod shadow}} = \frac{\text{Flagpole height}}{\text{Flagpole shadow}}$

$\frac{42}{14} = \frac{h}{42}$

Cross-multiply and solve:

$h = \frac{42 \times 42}{14} = \frac{1,764}{14} = 126 \text{ feet}$