Quite easy. We start by looking at the second ratio.

For Room B, Basketball : Soccer Ball = 4 : 9

This is after 4 basketballs have been loaned out.

So we can say that in room B , before the 4 basketballs were loaned out ,

Basketball = 4 units + 4
Soccer ball = 9


Now since ¼ of the basket balls in Room A were transferred to room B

Total number of basket balls at first
= 4 × (4 units + 4) = 16 units + 16

Number of basket balls left in Room A after the
transfer
= ¾ of all basketballs
= 3 × (4 units + 4) = 12 units + 12

We also notice that ¾ of all the soccer balls were left in room B. So that's 9 units

Soccer balls transfered to Room A = ¼ of all basketballs = 9 units ÷ 3 = 3 units


Soccer balls left in Room A after loaning out
= 3 units - 2


Then, go back to the first we see that the ratio of basketballs to soccer balls in room A is 6 : 1

Since there are 12 units + 12 basketballs here, number of soccer balls in room A after loaning out

= (12 units + 12) ÷ 6
= 2 units + 2

Then, we can say that :

2 units + 2 = 3 units - 2

Comparing them,

1 unit = 2 + 2 = 4

Number of soccer balls at first

= 12u
= 12 × 4 = 48