Anew crew of painters can paint a small apartment in 12 hours. an experienced crew can paint the small apartment in 6 hours. how many hours does it take to paint the apartment when the two crews work together?

This is the concept of proportionality, we are required to calculate for the number of hours two crews can use to paint the house altogether.
Here proceed as follows;
number of hours new crew can paint=12 hrs
portion of work painted by new crew in 1 hour= 1/12

number of hours experienced crew can paint=6 hours
Portion of work painted by experienced crew in 1 hour=1/6

Portion of work painted by the two crews altogether in 1 hour will be:
1/6+1/12=1/4

thus the total amount of hours that the two painters will take to paint will be:
4 hours

12