$\text{Total work} =\text{Efficiency (or) One day work}\times \text{Total time}$
$\textbf{W = DMTE}$
D = Number of days
M = Number of men
T = Number of hours per day
E = Efficiency
W = Amount of work
Now, $D_{1}M_{1} = D_{2}M_{2}$
$\implies \dfrac{\frac{4}{5}\times M_{1}}{\frac{1}{2} W} = \dfrac{1 \times M_{2}}{W}$
$\implies 8M_{1} = 5 M_{2}$
$\implies M_{1} = \dfrac{5}{8}M_{2}$
again, $x \times M_{2} = 16 \times (M_{1} + M_{2})$
$\implies x \times M_{2} = 16 \times \bigg(\dfrac{5}{8}M_{2} + M_{2}\bigg)$
$\implies x \times M_{2} = 16 \times \dfrac{13}{8}M_{2}$
$\therefore x = 26$ days