There are several ways to get to the answer.  

First way:
Since it takes 3 days for 10 workers to finish building one house, 
it would take those 10 workers 4 times that long to finish building 4 houses, so
it would take those 10 workers 12 days to finish building 4 houses.
It would take half as many workers twice as long to finish building 4 houses, so
it would take 5 workers 24 days to finish building 4 houses.
It would take 3 times as many workers as that only 1/3 as long to build 4 houses. So,
It would take 15 workers only 8 days to finish building 4 houses. 
  
Second way: 
Since it takes 3 days for 10 workers to finish building one house, 
it would take 3 times as many workers only 1/3 as long to finish building one house, so
it would take 30 workers only 1 day to finish building one house.
It would take half as many workers twice as long to finish building one house, so
it would take 15 workers 2 days to finish building one house.
It would take those 15 workers 4 times as long to finish building 4 houses. So,
It would take 15 workers only 8 days to finish building 4 houses.

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Still another way is to use the worker-jobs-time formula

W1 = number of workers in the first situation
T1 = time required in the first situation
J1 = number of jobs done in the first situation

W2 = number of workers in the second situation
T2 = time required in the second situation
J2 = number of jobs done in the second situation

The formula is













So it would take them 8 days.

Edwin