Elizabeth,

The short answer is that you can't do it exactly. The number of pairs of players you need to cover is 28 + 28 + 2x64 = 184 -- there are 28 pairs of old boys, 28 pairs of young boys, and 64 pairs consisting of one old boy and one young boy. Each foursome covers 6 pairs of players. Unfortunately 184 is not a multiple of 6, so an exact solution is not possible.

There is a well-known schedule where every pair of 16 golfers play together exactly once over 5 rounds. You can find that by searching the archive for golf 16. A good way to go would be to use that schedule for the first 5 rounds, and then in the last 2 rounds try to put together players who'd most like to be together twice.

Good luck!
--Victoria