Convert decimal 164 to binary, octal and hexadecimal.

$164 \div 8 = 20$ with a remainder of 4.
(Your work shows a remainder of 6, which is incorrect. $8 \times 20 = 160$, so $164 - 160 = 4$.)

$20 \div 8 = 2$ with a remainder of 4.

$2 \div 8 = 0$ with a remainder of 2.

Now, read the remainders from bottom to top: $2, 4, 4$.
So, $164_{10} = 244_8$.

Your answer of $(24)_8$ is incorrect because of the error in the first division's remainder.

The final answer is $\boxed{244_8}$.

Decimal to Hexadecimal Conversion ($164_{10}$ to Hexadecimal)

To convert a decimal number to hexadecimal, we repeatedly divide the decimal number by 16 and record the remainders. Remember that remainders 10-15 are represented by letters A-F.

$164 \div 16 = 10$ with a remainder of 4.
(Your work shows a quotient of 2, which is incorrect. $16 \times 10 = 160$, so $164 - 160 = 4$.)

$10 \div 16 = 0$ with a remainder of 10.
In hexadecimal, the digit 10 is represented by 'A'.

Now, read the remainders from bottom to top: $A, 4$.
So, $164_{10} = A4_{16}$.

Your answer of $(24)_{16}$ is incorrect because of the error in the first division's quotient and the resulting hexadecimal digit.

The final answer is $\boxed{A4_{16}}$.