Two identical brass balls mounted on a wooden posts initially have different amounts of charge, one +3.9 uc and the other +16.4 uc. the balls are allowed to touch and then separated again.

what is the final charge on each ball?

Use the law of conservation of charge: charge is always conserved. Here the system is the two balls, then the total initial charge of the two balls is the same of the total final charge of the two balls, which is +3.9 uC + 16.4 uC  = +20.3uC.

When the balls are in contact, they behave as one alone piece and the total charge is evenly distributed among the whole surface. Given that the two balls are identical (same shape and same size) every ball support half of the charge.

Then, when the two balls are separated again each will have (+20.3 / 2) uC = 10.15 uC