Add water to a solution and one thing refuses to change: the moles of solute. Water brings volume and nothing else — every particle that was in the flask is still in the flask. Since $C \, V$ counts those moles, the count before must equal the count after: $C_1 V_1 = C_2 V_2$ — read aloud, C-one V-one equals C-two V-two. That conservation IS the whole equation; there is nothing else to memorize.

Two courtesies the equation extends. First, the volume units cancel across the equals sign, so millilitres may stay millilitres — matching units on both sides is all it asks. Second, a sanity rail for free: water only ever lowers concentration. If your diluted answer comes out stronger than the stock, a subscript has swapped somewhere — no appeal.