Given: $3798125P369$ is divisible by 7

Let's express the given number in terms of triplets of digits, starting from the right, as follows: $(37) (981) (25P) (369)$

Now, $369-25P + 981 – 37 = 1350 – 25P – 37 = 1313 – 25P$

By dividing 1313 by 7 we get 4 as remainder.

$25P$ in the above equation should be in between 250 to 259. Now, 252 and 259 are divisible by 7. So, the number must be $252 + 4 = 256$.

Hence, value of $P = 6$

Let's double check it: $1313-256 = 1057$ It is divisible by 7.

Hence, option (B) is the correct answer.