Do you have to motivate the derivative with a difference quotient or are you allowed to use the "known" rules which follows from the definition? If you know the rules you have

s(t) = 4/t = 4*t^-1

s'(t) = -1*4*t^-2 = -4/t^2

If you have to use the limit of the difference quotient then we have the definition

s'(t) = lim(h->0) (s(t+h)-s(t))/h = lim(h->0) ((4/(t+h))-4/t)/h = lim(h->0) ((4t-4(t+h))/(t(t+h)))/h = lim(h->0) ((-4h))/(t(t+h)))/h = lim(h->0) ((-4))/(t(t+h)))/1 = -4/t^2

So we have the derivative

s'(t) = -4/t^2

Calculating the velocity at a = 2 were t = a

s'(t) = -4/t^2 => s'(2) = -4/2^2 = -1 m/s

I leave a = 4 as exercise for you.