AbstractA hexagon quadrangle system of order n and index ρ [HQSρ(n)] is a pair (X,H), where X is a finite set of n vertices and H is a collection of edge disjoint hexagon quadrangles (called blocks) which partitions the edge set of ρKn, with vertex set X. A hexagon quadrangle system is said to be a 4-nesting [N(4)-HQS] if the collection of all the 4-cycles contained in the hexagon quadrangles is a ρ/2-fold 4-cycle system. It is said to be a 6-nesting [N(6)-HQS] if the collection of 6-cycles contained in the hexagon quadrangles is a (3ϱ4)-fold 6-cycle system. It is said to be a (4,6)-nesting, briefly a N(4,6)-HQS, if it is both a 4-nesting and a 6-nesting.In this paper we determine completely the spectrum of N(4,6)-HQS for λ=6h, μ=4h and ρ=8h, h positive integer.