The first part is actually irrelevant to solving this question.

If there are 20 more boys than girls in the first group, and 12 more girls than boys in the second group , then

20 - 12 = 8

Overall there are 8 more boys than girls. The difference between their numbers is 8.

Since 45% of participants are girls,
100% - 45% = 55%

55% of participants are boys.

Difference = 55% - 45% = 10%

So 10% →8 people

55% → 8 people x 55/10 = 44

There were 44 boys

How to make sense of this :

Let the number of girls in the first group be 1 unit.

Then number of boys in the first group
= 1 unit + 20


Let the number of boys in the second group be 1 part.

Then number of girls in the second group
= 1 part + 12

Total number of girls = 1 unit + 1 part + 12
Total number of boys = 1 unit + 1 part + 20

Difference = 20 - 12 = 8

So overall there are 8 more boys than girls.

You will get the same result with model drawing. This is just the word equivalent of model drawing