Maybe what's happening here, assuming that you did match the speeds and types right, is that the system with 4+2 is running in single channel mode for 6GB since the memory capacities of the channels don't match. The motherboard is probably designed to run single channel asymmetrical mode if the modules in a bank don't match, but dual channel if they match. With two 8's added in, it might not no how to handle it (e.g., 4/8/2/8, which would be a bit of a jumble banks versus channels).
If you just put in your 8+8 in slots 0 and 2, it will run dual channel mode for 16GB.
So you could replace the 2 with another new 4GB module and run 8/4/8/4. That will give you 24GB dual channel mode (I think) since you'd be running an 8+4 in each channel (each channel consisting of two slots, low slot in one color, high slot in the other).
Or for kicks maybe try 4/8/8/blank and see if that gives you 20GB in single channel asymmetric mode.