The Volume of the cone shown is 6 cubic inches. What is the height of a cone with the same base diameter but a volume of only 3 cubic inches?

we know that
 [volume of the cone]=(1/3)*area of the base*height
h-----> height 
AB-----> area of the base
so
[volume of the original cone]=(1/3)*AB*h
volume=6 in³
(1/3)*AB*h=6--------> h=18/AB

For a cone with the same base diameter but a volume of only 3 cubic inches
(1/3)*AB*h=3 in³-------> h=9*AB

the answer is
The new cone height is half the original height