Good question. Whey you say, "so using substitution [s'] =< [t']", do you mean, that, since [s] is [s'], [t] is [t'] and [s] is known to be <= [t], we get [s'] <= [t']? The problem with this is that, well, <= on classes is not well defined. Indeed, given two equivalence classes A and B, how do you choose the representatives? Suppose you have some way; for example, if we are talking about numbers, choose the least prime numbers in A and B and compare them. Then it does not matter what the relationship is between R, which is used to compare representatives, and the ~, which is used to form equivalence classes. However, it may be the case that A <= B, s in A, t in B and ~Rst.
You are asked to show precisely that this situation is impossible. Namely, that for any s ~ s' in A and t ~ t' in B, Rst iff Rs't'. This requires using the relationship between ~ and R, as well as properties of R.