What is a two digit number that is four times the sum of its digits it is also equal to three times the product of its digits?

The two-digit number that fits the described criteria is 24.

Verification

Let's verify that 24 satisfies the two conditions:

• Condition 1: The number is four times the sum of its digits.

  • Sum of digits: 2 + 4 = 6
  • Four times the sum: 4 * 6 = 24
  • This condition is satisfied.

• Condition 2: The number is three times the product of its digits.

  • Product of digits: 2 * 4 = 8
  • Three times the product: 3 * 8 = 24
  • This condition is also satisfied.

Therefore, 24 is indeed the correct answer.