So in your orange paint, the ratio of red paint to yellow paint is 2/3 : 4/5, we can simplify that to 2/3 (15) : 4/5 (15) ---> 10 : 12 ---> 5 : 6. So for every 5 parts of red paint, you need 6 parts of yellow paint. One part can be any amount, as long as all parts are equal. So together you need 5+6=11 parts. Lets divide 88 by 11 to get what one part is. 88/11=8, so in this case one part equals to 8 bottles. And remember you need 5 parts of red paint, so 5*8=40 bottles of red paint altogether, and 6 parts of yellow paint, so 6*8=48 bottles of yellow paint altogether to make your 88 bottles of orange pain.
Check: 40 bottles of paint + 48 bottles of paint will give you 88 bottles of paint in the end, so that is correct. 40 : 48 is also equal to 2/3 : 4/5 if you simplify them, so the ratio is also correct.