The key to mapping here is the recognition that one reactant contains a five-carbon chain and the other a three-carbon chain. Chains of these lengths are also found in the product - but not where we might might anticipate them to be on first inspection. (Since the propanediol is symmetrical, the mapping of atoms 6, 7, and 8 can be reversed.) Thus, we need to find a way to bond the oxygens from the propanediol to C-5, and break C-5 loose from the oxygen it is originally attached to.

I have put the quotation marks around the "H⁺" used by the authors of this equation to indicate what we all know: no such thing really exists. This is simply a shorthand for any proton donor species. In this case, toluenesulfonic acid is a like source, since it is widely used to catalyze acetal formation.