Explanation:

6 is an even multiple of 3. When any even multiple of 3 is divided by 6, it will leave a remainder of 0. Or in other words it is perfectly divisible by 6.

On the contrary, when any odd multiple of 3 is divided by 6, it will leave a remainder of 3. For e.g when 9 an odd multiple of 3 is divided by 6, you will get a remainder of 3.

9 is an odd multiple of 3. And all powers of 9 are odd multiples of 3.
Therefore, when each of the 8 powers of 9 listed above is divided by 6, each of them will leave a remainder of 3.

The total value of the remainder =3+3+....+3 (8 remainders) = 24.
24 is divisible by 6. Hence, it will leave no remainder.

Hence, the final remainder when the above expression is divided by 6 will be equal to '0'.