Learn Turkish: Bu eski oyuncakları kaldırayım. - Let me put away these old toys.

The verb root is kaldır- (to put away / to lift). To express "let me" or "I will", we add the optative suffix -a followed by the 1st person singular ending -yım to make kaldırayım.

If bu means "this", why does the English translation say "these"?

In Turkish, demonstrative words don't take plural markers when used before a noun. The word bu stays singular even when describing plural nouns. The plural meaning is shown entirely by the -lar suffix on oyuncakları (toys).

Why is there an -ı at the end of oyuncakları?

That is the accusative case suffix. Whenever a direct object is specific (which is triggered here by the pointing word bu), it needs the accusative ending. Oyuncaklar (toys) becomes oyuncakları to show we mean "these specific toys" that are being acted upon.

Doesn't the k in oyuncak usually change to a ğ when adding suffixes? Why didn't it happen here?