Painting houses

If 3 painters can paint 2 houses and 2 sheds in a day and a house and 10 sheds in 2 days, then 3 painters can paint 2 houses and 20 sheds in 4 days, i.e. (by substraction) they can paint 18 sheds in 3 days which is the same as 6 sheds in 1 day.

By another substitution, we find that they can paint 3 house in a day and so 5 houses in $\frac{5}{3}$ days.

So to paint 5 houses and 6 sheds they need $1 + \frac{5}{3} = \frac{8}{3}$ days. For 2 painters, the total duration is thus $\frac{3}{2} \times \frac{8}{3} = \frac{8}{2} = 4$ days.