The first part of the question is telling you that both had the same number of sweets and chocolates at first after they gave each other.

After eating 12 sweets, ratio of sweets to chocolates Jim had = 1 : 7

So Jim's sweets = 1u
Jim's chocolates = 7u

After eating 18 chocolates, ratio of sweets to chocolates Ken had = 1 : 4

Realise that Ken didn't eat any sweets. So his number of sweets is just the original number he was given. It is the same number of sweets Jim had before he ate those 12 sweets.

Ken's sweets = 1u + 12
So Ken's chocolates = 4 x (1u + 12)
= 4u + 48

Now since Ken ate 18 chocolates, number of chocolates he had at first
= 4u + 48 + 18
= 4u + 66

This is the same number of chocolates Jim had since Jim didn't eat any chocolates.

So 7u = 4u + 66
3u = 66
1u = 66 ÷ 3 = 22

So sweets that Ken had = 1u + 12
= 22 + 12
= 34

Since each had same number of sweets, number of sweets Jim bought is twice of what Ken had
= 34 x 2
= 68