Snowman's Lost His Head is the fifth mission of Cool, Cool Mountain.
The yellow sphere is the anti-cheat checkpoint Mario must touch in order for the race to count.
The green sphere is where Mario must be standing for the head to bump into the body.
Example with Input Display
Avoid sliding on the darker, gray spots here; doing so will slow you down and may prevent you from getting in front of the snowball.
Animation Skip "Tutorial"
This video does a double jump kick, but you can do the backflip setup as well.