This type of problem is a Work Problem.

We can solve this problem by using the formula

1/x + 1/y = 1/z,

where; x = time taken by Sonny

y = time taken by his brother

z = time taken by Sonny and his brother

The given in the problem is the time taken by Sonny which is 15 days and the time taken by both of them is 4 days

Since Sonny worked for 6 days already instead of 15 days, he has supposed to have remaining of 9 days to do the job alone but his brother helped him so they do the job together for 4 days only instead of 9 days.

We will now look for the time his brother do the job alone

1/x + 1/y = 1/z

1/9 + 1/y = 1/4

1/y = 1/4 - 1/9

1/y = (9-4)/36

1/y = 5/36

5y = 36

y = 36/5

y = 7.2

Therefore, Sonny's brother will take 7.2 days to do the job alone