Let the unit digit of the number is x and tens digit of the number is y

So, the number is 10y + x

Given, the product of 2 digits of the number is 24

=> x*y = 24  ..................1

Again given its units digit exceed twice its tens digit by 2

=> x = 2y + 2

From equation 1, we get

     (2y + 2)y = 24

=> 2y² + 2y = 24

=> 2(y² + y) = 24

=> y² + y = 24/2

=> y² + y = 12

=> y² + y - 12 = 0

=> (y + 4)*(y - 3) = 0

=> y = 3, -4

Since y = -4 is not possible.

So y = 3

Now, from equation 1, we get

=> x * 3 = 24

=> x = 24/3

=> x = 8

So, the number is 38