Which PDP-8 is this? (ebay: 261232211533)

I think we're all "right", depending on which gizmo we are describing :-). The bare PDP-8/L has a maximum of 4K. The BA08 adds 4K for a maximum of 8K. The BM08 adds up to 8K for a maximum of 12K. (According to the OS/8 support manual, it actually inhibits CDF instructions for fields >2, treating them as a NOP.) The BM8L adds up to 28K for a maximum of 32K. (It extends the IF and DF to the full 3 bits, so I'm quite sure it goes beyond 16K.) At most one of the memory expansions is permitted, since they conflict about their implementation of the extended memory control. Since the expansion boxes seem to have been introduced at various times, documentation for the PDP-8/L differs about whether 8K or 12K is the maximum. The BM8L is fairly rare. I think it was introduced near the end of the life of the 8/L, and I don't think I've ever even seen it discussed in an 8/L manual.