"He can memorize a book."
Translation:Li povas parkerigi libron.
The root is "parkere", which means "from memory" or "by heart". Most dictionaries will tell you that the correct way to form the word "to memorize" from this root is to add -ig- and get "parkerigi", whereas a lot of Esperanto speakers just change the adverb directly to a verb and get "parkeri".
parkeri is an intransitive verb. "Mi parkeras." ("I memorize.") There is no object. To turn the verb into a transitive verb, Esperanto adds -ig-. "Mi parkerigas libron." ("I am memorizing a book.") This can be done with any intransitive verb as long as the result make sense.
I still don't see why -ig- would be used here ;-; Some explanations I saw were saying that -ig- is used when you want to turn something into something else. It makes sense in "Mi limpigas mia salonon" (I will make the living room get clean, to clean) and "Mi mortigos vin." (I'll make you get dead, to kill). But "He can turn a book memorized" doesn't make any sense to me.
Parkeri means parkere scii (know by heart). So parkerigi means to make known by heart, or in English natural idiom, to memorize. So, "li povas parkeri libron" would mean, "he can know a book by heart," which doesn't make much sense, at least to me. But "li povas parkerigi libron" means, "he can memorize a book," which does make sense.