56 в Б

Let the number of lollipops in box B at first be x, then the number of lollipops in box A at first will be 196 – x.

The question says this:

There were 24 more lollipops in box A than in box B after 32 lollipops were transferred from box A to box B. 

Let’s understand the part where lollipops were transferred. This means that 32 lollipops are subtracted from box A and 32 lollipops are added to box B. We can write it as this:

box A – 32, box b + 32

And then we have this:

196 – x – 32, x + 32

We know that after this, there are 24 more lollipops in box A than in box B, so after transferring, box A = box B + 24

196 – x – 32 = x + 32 + 24

164 – x = x + 56

2x = 108

x = 54

The number of lollipops in box B at first is 54.