Explanation:

To determine if 72k460k is divisible by 6:

- Divisibility Rule for 6: A number is divisible by 6 if it is divisible by both 2 and 3.

- Divisibility by 2: The last digit must be even. So, k must be even (0, 2, 4, 6, 8).

- Divisibility by 3: The sum of the digits must be divisible by 3. Sum is 7 + 2 + k + 4 + 6 + 0 + k = 19 + 2k.

Now, for each option:

- Option 1: k = 4

- Last digit = 4 (even)

- Sum = 19 + 8 = 27 (divisible by 3)

- Number is divisible by 6.

- Option 2: k = 7

- Last digit = 7 (odd)

- Number is not divisible by 2, hence not by 6.

- Option 3: k = 9

- Last digit = 9 (odd)

- Number is not divisible by 2, hence not by 6.

- Option 4: k = 8

- Last digit = 8 (even)

- Sum = 19 + 16 = 35 (not divisible by 3)

- Number is not divisible by 6.