First, establish how much paint you get from your mixture:
So each combination yields 2 full bottles of orange paint, with 7/15 of a bottle extra.
Since we need 88 bottles of orange paint,
Therefore, we need 60 batches of paint.
Multiplying through by 60 shows us that we will need
40 bottles of Red paint and 48 bottles of Yellow paint to yield 88 bottles of Orange paint