How did they meet?

The Altai Mountains sit in a region where, the genetics suggests, Neanderthal and Denisovan ranges overlapped.

Whether that overlap was extensive or limited, whether members of both groups were present in the same areas routinely or rarely, is not established by the current evidence.

What we can say is that at some point, a Neanderthal woman and a Denisovan man were in close enough proximity, and sufficiently compatible biologically and socially, to produce a child.

The child survived to at least the adolescent years.