When landing after a spectacular somersault, a 45.0 kg gymnast decelerates by pushing straight down on the mat. calculate the force she must exert if her deceleration is 8.00 times the acceleration of gravity.?

So the force that the gymnast with a mass m=45 kg, has to exert against the ground to stop if her acceleration is a=8*g, where g=9.81 m/s², can be obtained from the Newtons second law: F=m*a, where F is the force, m is the mass and a is acceleration. 

F=m*a=m*8*g=45*8*9.81=3531.6 N. 

So the force that a gymnast has to exert on the mat in order to stop is F=3531.6 N.