What is your question? You are told exactly what to do!
You are told that the equation must be of the form
S= at2+ bt+ c.
You are given t and S values for 6 different values of t.
Putting the given x and t values into the equation above for 3 different values of t (t= 0, 2, 3, as they suggest, will do but the choice is yours) will give you 3 equations to solve for a, b, and c. (Taking t= 0 will get an especially easy equation!)