One of my friends was struggling in understanding the definition of epsilon-delta definition of limits. Now he finally got the meaning of the definition. Now when we were using this definition as here(see example 2). Here we first start from the right-hand side of the implication and then we simplify it and get something which looks like the left-hand side of implication and then we say that let $\delta=f(\epsilon)$ (some function of $\epsilon$). And now finally we start from left side of implication and reach to the right-hand side of the implication.
My friend is getting a problem in understanding that why we do the first process i.e. simplify the right side of the implication.
One day I was playing this game and then I thought that I can use it to clear my friends doubt but I don't know how.
Please help me in order to clear my friends doubt either by the help of the game above or by any other example.