Since the example in the question was transmitted without error, we know even parity is being used. This just means for each of the answer options after you add on the parity bit to the digits given, you need to count the amount of 1's and see if the sum is even or odd. If the sum of 1's is odd, an error occurred since even parity is being used. If the sum was even, the message went fine.
For option A : 01010111 (Parity Bit 1) it becomes 010101111 after adding the parity bit. There are six 1's which is an even sum and that means no error occurred.
For option B: 01100101 (Parity Bit 1) it becomes 011001011 after adding the parity bit. Now there are five 1's, but this is an odd sum and since even parity is being used, as error must have occurred.
So Answer is B