Cheers,
it's a bit unclear (to me): do you have two Aruba 5406R zl2 and two Aruba 3810M (this pair depolyed with hardware stacking modules and stacking cables)?
If so you can stack together both Aruba 3810M (that is known as backplane stacking), the Aruba 5406R zl2 Switches' pair can be "stacked" together through the deployment of VSF technology (which is known as frontplane stacking), VSF doesn't require dedicated stacking hardware but has strict requirements about Hardware modules installed into Aruba 5400R zl2 (v3 zl2) and software mode of operation of the Switch.
You can then interconnect both pairs (2 x Aruba 3810M and 2 x Aruba 5406R zl2) by using a Port Aggregation (with LACP I suggest), that's if you need...but this doesn't mean "stacking" those two pairs (which CAN'T be done)...it's just deploy an (aggregated) uplink between those two pairs.
Keep in mind that each pair of Switches is and behaves like a single logical Switch (even if it's made of two physical Switches).