Give examples to show that f ◦ g and g ◦ f are distinct.

how do i come up with examples to prove that this is true

Let f(x) = 3x and g(x) = x^2.

f(g(x)) = f(x^2) = 3x^2

g(f(x)) = g(3x) = (3x)^2 = 9x^2

There are many more examples, but here is one.

Pick almost any two functions and compose them both ways, and you'll probably have your example. For instance, if f(x) = x² and g(x) = x+1, then (f◦g)(x) = (x+1)², but (g◦f)(x) = x²+1. These are clearly two different functions.

let f = x^2 and g = 2x

then
f ◦ g = (2x)^2 = 4x^2

but

g ◦ f = 2(x^2) = 2x^2