Option 4 : i and iv

Concept used:

Divisibility rule of 6 = If the number is divisible by 2 and 3 both then that number is also divisible by 6

Divisibility by 2 = If the unit digit of the number is 0, 2, 4, 6, and 8 then the number is divisible by 2

Divisibility by 3 = If the sum of the number is divisible by 3 then the number is also divisible by 3

Calculation:

Checking options one by one

All the given number is divisible by 2 so we will check the divisibility by 3 only. In this case if the number is divisible by 3 then the number is also divisible by 6

i) 5994 = 5 + 9 + 9 + 4 = 27 it is divisible by 3

∴ 5994 is also divisible by 3

So 5994 is divisible by 6

ii) 8668 = 8 + 6 + 6 + 7 = 28 it is divisible by 3

∴ 8668 is not divisible by 3

So 8668 is not divisible by 6

iii) 5986 = 5 + 9 + 8 + 6 = 28 it is not divisible by 3

∴ 5986 is not divisible by 3

So 5986 is not divisible by 6

iv) 8982 = 8 + 9 + 8 + 2 = 27 it is divisible by 3

∴ 8982 is also divisible by 3

So 8982 is divisible by 6

∴ The correct answer is option 4