To find the cost of putting a new floor in Greta's closet, we first need to calculate the area of the closet.
The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{width} \]
In this case, the length is 3 feet and the width is 2 feet. So the area is:
\[ A = 3 , \text{feet} \times 2 , \text{feet} = 6 , \text{square feet} \]
Next, we need to calculate the cost of flooring. The cost per square foot is $4.38. Therefore, the total cost \( C \) is given by:
\[ C = \text{Area} \times \text{Cost per square foot} \]
Substituting the values we have:
\[ C = 6 , \text{square feet} \times 4.38 , \text{dollars per square foot} = 26.28 , \text{dollars} \]
Thus, the total cost to put a new floor in the closet is \(\boxed{26.28}\) dollars.