An ideal gain block multiplies its input by the declared gain, so the voltage contract is checked before later limits or loading are considered. The 4 V input with gain 2 gives 8 V exactly in this model; real gain stages add input offset, gain error, finite bandwidth, slew limits, rail headroom, loading, noise, temperature drift, and voltage/time measurement uncertainty.
An ideal gain block multiplies voltage by the declared exact gain. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.