Understand the divisibility rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.

Calculate the sum of the known digits: Add the digits of 4252746: $4+2+5+2+7+4+6=30$

Determine the required sum for divisibility by 3: For the number to be divisible by 3, the total sum of its digits (including $B$) must be a multiple of 3.

Set up the equation: Let $B$ represent the unknown digit. The total sum of the digits is $30+B$. For divisibility by 3, $30+B$ must be divisible by 3.

Solve for possible values of $B$: Since 30 leaves a remainder of 0 when divided by 3, $B$ must also be a multiple of 3 for $30+B$ to be divisible by 3. The possible values of $B$ are 0, 3, 6, and 9.

Conclusion: There are 4 possible values for $B$ (0, 3, 6, and 9) that make the number 4252746 $B$ divisible by 3. Therefore, the correct answer is C. 4.