Find the value of P such that 4864 imes 9P2 is divisible by 12.

A number is divisible by 12 if it is divisible by both 3 and 4.

For a number to be divisible by 4, the number formed by its last two digits must be divisible by 4.
The number 4864 is divisible by 4 because its last two digits, 64, are divisible by 4 ($64 \div 4 = 16$).
Therefore, for the product $4864 \times 9P2$ to be divisible by 4, $9P2$ must be divisible by 4.