Must be tricky. OK, I'll bite.

Volume of cylinder and water together = pi(r^2)h = pi(16)(6/pi) = 96 cubic inches

Volume of cylinder = pi(3^2)(6/pi) = 54 cubic inches

Therefore, volume of water = 42 cubic inches.

H after cylinder removed = 42/(pi(4^2) = [spoiler]21/pi(8)[/spoiler]

Another, more direct, approach.

What is the volume of water directly ? Area of surface x height

Area of surface = length x width > width is difference in radii > =1"

Length is trickier: It's the average of the length of the inner radius and the outer radius

Length = 2(pi)[(3+4)/2)] = 7(pi)

Surface Area = Length x width = 7(pi) x 1 = 7(pi) square inches

Volume = Surface area x height = 7(pi) x (6/pi) = 42 cubic inches

New height of water = Volume/area = 42/16(pi)=

D