Proportion of deer population is given as

$$ \frac{Tagged\ deer\ in\ capture\ 1}{Deer\ population}=\frac{Tagged\ deer\ in\ capture\ 2}{Deer\ in\ capture\ 2} $$

$$ \frac{108}{Deer\ population}=\frac{36}{54} $$

$$ {Deer\ population}=\frac{108\times 54}{36}=162 $$