The amount of pure alcohol in 200mL of a 75% solution is 150mL.
x mL of a 60% solution contains 0.6x pure alcohol. If we add y mL of pure alcohol we end up with 0.6x+y mL of alcohol so 0.6x+y=150.
Also x+y=200, the combined quantity in the mixture. Therefore y=200-x.
So 0.6x+200-x=150, 0.4x=50, x=50/0.4=125mL, y=200-125=75mL.
So we need 125mL of 60% solution and 75mL of pure alcohol.