Looks like a classic use of F = ma
The mass is given in the problem as 25.0 kg.
The acceleration you can find quickly if you know that the acceleration of gravity ("g") = 9.81 m/s2. This makes the gymnast's acceleration = 68.67 m/s2
Now we can just plug back in:
F = (25.0kg) * (68.67 m/s2)
F = 1716.75 N downwards
Keeping the 3 significant digits, the most appropriate answer would be F = 1720 N downwards
1) Remember that force is a vector, so your answer needs to have a magnitude (aka a number) and a direction. If you don't need a direction, the question will usually say "find the magnitude".
2) The force from the ground is equal an opposite to your answer, so 1720 N upwards.
3) Significant figures: You can google the rules, but the general idea is to be as precise as the given data. So, don't write your answers to 5 decimal points and don't round more than necessary.