I is it true that the product of two mixed numbers that are each between four and five is between 16 and 25

Yes

the boundaries are 4 and 5

the smallest mixed number approaches 4

if we assume 4 then

4²=16

that is minimum, but it has to be slightly greater than 4 at least, so the product will be slightly greater than 16

the larges mixed number approaches 5

if we assume 4 then

5²=25

that is maximum, but it has to be slightly less than 5 at most, so the product will be slightly less than 25