You can listen to the entire conversation
here.
The broader context is Reagan trying to sell Nixon on some sort of passive-aggressive anti-UN strategy, where the US still shows up for the debates and whatnot, but doesn't actually vote, or obey the results of the votes. Nixon seems to evince muted skepticism about this idea, pointing out that the UN still performs useful functions for the USA, and gives India/Pakistan as his example.
Reagan had apparently returned from as Asian visit, where among other things, he met Chiang Kai Shek.
At one point, Nixon asks Reagan, somewhat sheepishly, for confirmation that the Vietnam War is going well, and Reagan assures him it is, and then Nixon congratulates himself for the US enduring only six casualties that week. It occurs to me that the families of those six, if they now listen to this tape, could calculate that it was their son among those being discussed.