Closed-loop gain first computes the requested output, but the supply rails decide whether that voltage is actually available. The 15 V request clipping to 12 V is an ideal rail-limit ledger; real saturation depends on output stage headroom, load current, recovery time, temperature, device variation, and measurement tolerance.
Closed-loop gain is checked first, then rails clip unavailable output. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Closed-loop gain gives a requested output first
Gain 3 times 5 volts requests 15 volts.
3⋅5V=15V
The rail decides what output is available
The available output clips to 12 volts, leaving the feedback node at 4 volts instead of 5 volts.