Almost $$2$$2-perfect $$6$$6-cycle systems

We prove that an almost $$2$$2-perfect $$6$$6-cycle system of order $$n$$n exists if and only if $$n \equiv 1$$n≡1 or $$9\ (mod\ 12)$$9(mod12), and that an almost $$2$$2-perfect maximum packing with $$6$$6-cycles of order $$n$$n exists for all $$n \ge 6$$n≥6.