Question

A four digit number is between 3,000 and 4,000.The sum of its digits is 21.The product of the thousand and ones digits 24.The hundreds digit.What is the number?

Answer 1

So...
Your number is between 3000 and 4000
The sum of its digits is 21.
The product of the thousand and ones digits 24.

Answer 2

What about the hundreds digit?

Answer 3

Consider the number to be ABCD
We know that A = 3
so 3+B+C+D = 21
B+C+D = 17
"The product of the thousand and ones digits 24" ==== 3*D = 24
D = 8
That leaves B+C = 9

Once you have decided what the story is with the hundreds digit,
you will be able to finish it

so far we have:
3BC8 , where B+C = 9