How can best glide speed be lower than best rate of climb speed?
The best glide speed is the speed where tangent line from the origin (zero horizontal and vertical speed) touches power curve (for unpowered airplane).

Best rate of the climb is the highest point of the power curve.

When we start with unpowered airplane, the direct equivalent of best rate of climb is lowest rate of sink. The speed for lowest sink will be clearly lower than the best glide speed.

If we would assume that aircraft engine is a magical device, which simply adds some fixed amount of mechanical energy to the airplane regardless of what, then the "powered" power curve would be simply the "unpowered" one shifted up in the graph. Under such assumptions the speed for best climb would be the same as the speed for minimum sink and in both cases lower than best glide speed.



Nevertheless mentioned Cessna converts fuel to mechanical energy through not-so-magical fixed pitch propeller which pushes some amount of air around. Such propeller would be typically optimized for highest efficiency at the cruise speed, so with decreasing speed the amount of available mechanical energy dereases. Which results in changed shape of power curve and maximum point moves towards higher speeds compared to the "unpowered" power curve.



This shift can be high enough that Vy ends up higher than Vg.

The Vy is always higher than the speed for the best climb angle, because these two speeds are found on the same (max power) power curve. For the same reason best glide speed will be always higher than speed for minimum sink. But speeds for best rate of climb and for the least sink does not need to be the same because of effects of real propeller.

For related images and more information, have a look at great online text See How It Flies.