  We design a fully polynomial time approximation scheme (FPTAS) for counting
the number of matchings (packings) in arbitrary 3-uniform hypergraphs of
maximum degree three, referred to as $(3,3)$-hypergraphs. It is the first
polynomial time approximation scheme for that problem, which includes also, as
a special case, the 3D Matching counting problem for 3-partite
$(3,3)$-hypergraphs. The proof technique of this paper uses the general
correlation decay technique and a new combinatorial analysis of the underlying
structures of the intersection graphs. The proof method could be also of
independent interest.
