Place Value Puzzle: Finding Numbers with 4 in Thousands and Smaller Hundreds Digit

To solve this problem, let's start by considering the criteria:

• The thousands digit of the number must be 4, which represents values in the format $4XXX$.
• The hundreds digit must be less than 4, meaning it can be 0, 1, 2, or 3.

Given these constraints, let's consider the provided choices:

1. $4321$:
   - Thousands digit is 4.
   - Hundreds digit is 3 (which is less than 4).
   - This choice satisfies both conditions.
2. $3321$:
   - Thousands digit is 3.
   - This does not satisfy the condition of having a thousands digit of 4. Therefore, it's incorrect.
3. $1200$:
   - Thousands digit is 1.
   - This does not satisfy the condition of having a thousands digit of 4. Therefore, it's incorrect.
4. $4789$:
   - Thousands digit is 4.
   - Hundreds digit is 7 (which is not less than 4).
   - This choice does not satisfy the condition of having a hundreds digit less than the thousands digit. Therefore, it's incorrect.

Therefore, the number that meets all the conditions is $4321$.