Answer:
16:6
Step-by-step explanation:
I would first see if there are any common factors.

Common factors for both 96 and 36 are 12, 6, 4, 3, and 2.
96 orange shirts : 36 purple shirts
48 orange shirts : 18 purple shirts
24 orange shirts : 9 purple shirts
Get to the lowest numbers which would be...
16 orange shirts to 6 purple shirts.
Factors are whole numbers that are multiplied together to produce another number. The original numbers are factors of the product number.