$s(t)$ is the position at time $t$.
The velocity is the rate of change of the position.
So the velocity at time $t$ is $s'(t)$.
You want to find the value of $t$ at which $s'(t) = 20$.
So... you find $s'(t)$; you set it equal to $20$. And...
Added. And you've added an entirely new question in comments, after requesting here in comments that you be given an answer to the mystery question you kept hidden....
The acceleration is the derivative of the velocity; the velocity is the derivative of the position. So the acceleration is the second derivative of the position (something that I am positive is in whatever book you are trying to learn from; are you actually reading the material and trying to understand it, or are you rushing to the exercises and then just asking for the solutions here?).
To find the times when the acceleration has a particular value $a$, you find the acceleration function by computing $s''(t)$, set $s''(t)$ equal to $a$, and solve for $t$.