72 + 16 = 96 (Explanation for the curious)

Yeah, um, that was me trying to hid some stuff from you and forgetting what I was glossing over. If you are interested:

Some x86-64 instructions are very complex. They are translated into simpler operations in hardware. In recitation we saw that a mov that references memory is translated into multiple simple operations in the underlying hardware, the mov and the memory reference. The mov is dependent upon the memory reference. These smaller instructions are called micro-operations.

There are 16 architectural registers and 72 re-order buffer entries. That is 88 registers. But there are also 8 hidden registers that are used for shuffling values between micro-operations. These are not part of architectural state (the state the asm programmer sees) but they are needed to shuffle values between micro-ops when a dependent micro-op is evicted from the re-order buffer.