The average force necessary to stop a bullet of mass 20 g moving with a speed of $250m{s}^{-1}$, as it penetrates into the wood for a distance of 12 cm is:

Final speed $\left(v\right)=0$
Step2: Formula used
To compute the acceleration, use the third equation of motion $v^2=u^2+2as$
Where v= final speed, $u=$ initial speed, $a=$ acceleration, and $s=$ distance.
Step3: Determine the acceleration
Substitute the known values in the formula, $v^2=u^2+2as$
$(0{)}^2=(250{)}^2+2a\times (0.12)$
$-62500=0.24\times a$
$a=-\frac{62500}{0.24} \mathrm{m}/{\mathrm{s}}^2$
Acceleration is negative, it means it is acting in opposite direction.
Step4: Compute the force needed to stop the bullet
We know that $F=ma$. 

So,
 $F=\left(20\times {10}^{-3}\right)\times \frac{62500}{0.24}$
$F=5208.3 N$
Thus, the required force to stop the bullet is $5208.3 \mathrm{N}$.

Hence, the correct answer is option D.