If an opponent casts a spell with X in its mana cost, the converted mana cost of that spell takes the value of X into account. If you reveal a card with X in its mana cost, X is 0. For example, if your opponent casts Blaze with X=1, Counterbalance will counter that spell if you reveal a card with converted mana cost 2, but it won't counter that spell if you reveal a Blaze of your own.
If an opponent casts half of a split card (for example, Hit), it won't be countered if you reveal that same split card. The converted mana cost of a split card is determined by the combined mana cost of its two halves, but the converted mana cost of Hit is determined using only that half's mana cost.