if i could go back in time and tell my self about dihybrid crosses i would say that you use it for when you want to use it for more then one trait. for example you would use it for color and shape. this would make it easier then making 2 punnet squares. one for shape and one for color. this way you can determine what the chance is to have yellow skin with a square shape,etc. lastly it has to do with the parents genotype.

you might want to use this when you need to have multiple traits determined. for example, the possiblity that your child is going to have blonde hair and blue eyes or brown hair brown eyes.