Since all watermelons weigh the same and all cantaloupes weigh the same we can denote:

'w' to be the weight of 1 watermelon

'c' to be the weight of 1 cantaloupe

We need to find the weight of 2 watermelons and 1 cantaloupe that is 2w + c = ?

Using the conditions we have:

3w + 2c = 32 (3 watermelons and 2 cantaloupes weigh 32 pounds) (1)

4w + 3c = 44 (4 watermelons and 3 cantaloupes weigh 44 pounds) (2)

By multiplying the first equation by 2 (on the both sides) and subtracting the second equation we have:

2*(3w + 2c) - (4w + 3c) = 2*32 - 44

6w + 4c - 4w - 3c = 64 - 44

2w + c = 20

That is, the weight of 2 watermelons and 1 cantaloupe is 20 pounds.