If 2 men or 3 women or 4 boys can do a piece of work in 52 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in:

Work done by 2 men = 3 women = 4 boys
1 man = 2 boys
1 woman = $$\frac{4}{3}$$ boys
Thus,
Boys × days = 4 × 52 boys × days
Again,
1 man + 1 women + 1 boys,
$$ = 2 + \frac{4}{3} + 1$$
$$ = \frac{{13}}{3}$$  boys
Using work equivalent method,
boys × day = BOYS × DAYS
$$4 \times 52 = \frac{{13}}{3} \times {\text{x}}\,{\text{(let)}}$$
x = 48 days