Answer: Yes it is a four-digit whole number.
Step-by-step explanation
We will fill in these 4 blanks with digits:
_ _ _ _
It is greater than 4000.
It is less than 5000.
Therefore its thousands digit is 4
4 _ _ _
Its tens digit is 3.
So we have
4 _ 3 _
The product of its hundreds digit and its ones digit is 0.
Therefore it is either 4 0 3 _ or 4 _ 3 0
It is not an even number.
That rules out 4 _ 3 0 for that is even regardless of the hundreds digit
So we have
4 0 3 _
The sum of its hundreds digit and its ones digit is 9.
Therefore its ones digit is 9.
And the number is
4 0 3 9
We did not need this:
Twice its tens digit is 2 more than its thousands digit.
But that is true because twice 3 is 6 which is 2 more than 4
We also did not need this:
The sum of its hundreds digit and two- thirds of its ones digit is 6.
But that is true because 2/3 of 9 is 6.
We also did not need this:
Its tens digit is 1 less than its thousands digit.
But that is true because 3 is 1 less than 4
So we were given more information than we need