Learn Finnish: Näin hänet viimeksi viime kesänä.

The words viime (last) and ensi (next) are exceptions to the usual rule where modifiers match their nouns. They are indeclinable time modifiers, meaning they never change their form, no matter what case the following noun is in.

How do the words viimeksi and viime function differently here?

Viimeksi is an adverb that means "for the last time" or "most recently". Viime is an indeclinable modifier that means "last" or "previous" and must precede a time noun (like kesänä). Though they come from the same root, they play completely different roles in the sentence.

Why does kesä take the essive ending (-nä) here?

When expressing a specific point in time to answer "when?", Finnish frequently uses the essive case (-na / -nä). This is the standard grammatical case for seasons, days of the week, and holidays.

As a quick refresher, why is the object hänet instead of the partitive häntä?

The action of seeing him was a completed event, so the verb nähdä (to see) requires a total object. While most singular nouns look like the genitive when acting as a total object, personal pronouns like hän have a special accusative form ending in -t (hänet).