Learn Italian: Il motore è pulito, quindi lo continuo a rimontare. - The engine is clean, so I continue to reassemble it.

This is a great example of clitic climbing. With aspectual verbs like continuare a (to continue to), you have two options for placing object pronouns like lo. You can put the pronoun before the conjugated verb (lo continuo a rimontare) or attach it to the end of the infinitive (continuo a rimontarlo). Both are perfectly correct and mean the same thing.

Why do we need the preposition a after continuo?

The verb continuare requires the preposition a whenever it is followed by an infinitive verb to express "to continue doing something." Other aspectual verbs might use a different preposition, such as finire di (to finish doing).

Could I attach the pronoun lo to the preposition a?

No, object pronouns can never attach to prepositions like a or di. They must either attach to the end of an infinitive verb (dropping the final -e, creating rimontarlo) or stand alone before a conjugated verb (lo continuo).

What does the ri- prefix in rimontare do here?

Just like the English prefix "re-", the Italian prefix ri- means doing an action "again." While montare means "to assemble" or "to mount," rimontare means "to reassemble." This fits the context perfectly: the engine was taken apart to be cleaned, and now it is being put back together.