For a constant collector-emitter voltage of 8V , the collector...

Given here, ${V}_{CE} = 8V$, ${I}_{C} = 6mA$ from $4mA$ and ${I}_{B} = 20\muA$ to $25\muA$

Current gain is the ratio of change in output current divided by change in input current. For common CE (Common Emitter) configuration, it is the ratio of change in collector current divided by change in base current.

Current gain ${\beta}_{av} = \dfrac{{I}_{C} - ' {I}_{C}}{{I}_{B} - ' {I}_{B}} = \dfrac{\left(6 - 4\right)mA}{\left(25 - 20\right)\mu A} = \dfrac{2mA}{5\mu A}$

${\beta}_{av} = \dfrac{2}{5} \times {10}^{3} = \dfrac{2000}{5} = 400$