Enol and enolate mechanisms always involve the alpha position of the carbonyl (one away from the carbonyl carbon). This the alpha hydrogen is acidic, and so can be deprotonated.
To form an enol (or enolate) from a carbonyl, the alpha position of the carbonyl must be deprotonated, and the double bond (pi electrons) travels "goes up" to the oxygen to become a lone pair.
To form a carbonyl from an enol (or enolate), the alpha position of the carbonyl must be protonated, and a lone pair on the oxygen "comes down" to reform the carbonyl.
This "up and down" mechanism is similar to the Nucleophilic Acyl Addition/Substitution mechanisms discussed in problems 705 and 706, with the difference being that the carbon carbonyl is not where bond formation takes place. In enol/enolate mechanisms, new bond formation occurs at the alpha position.
a) Carbonyl to Enol (acidic) "UP"
Because this mechanism takes place under acidic conditions, the carbonyl oxygen must be protonated before its double bond "goes up" to form a lone pair.
b) Enol to Carbonyl (acidic) "DOWN"
Most people remember that a lone pair from the enol oxygen "comes down." But many forget that you have to add something back to the alpha position! In this case, it's just a hydrogen- you reprotonate the alpha position to form the carbonyl.