Option (a) ⇒ If the number is even meaning that if last digit is 0,2,4,6,8 than it is divisible by three.

Option (b) ⇒ The divisibility test of 3 says that if the sum of all the digits is divisible by three than the number is divisible by three. Therefore this option is correct.

Option (c) ⇒ If the number is divisible by both 3 and 2 than it is divisible by 6.

Option (d) ⇒ if the sum of all digits is divisible by 9 than the number is divisible by 9.