The closed-loop transfer function is $T(s)=K/(\tau s+1+K)$, with DC gain $K/(1+K)$. The observed final output for a step of height 10 is $10K/(1+K)=8$. Thus $10K=8+8K$, yielding K = 4. The time constant affects approach to the final value but is not needed for this gain.
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