Learn Turkish: Altıncı ay haziran. - The sixth month is June.

The root number is altı (six). To make an ordinal number (like first, second, or sixth), Turkish adds a suffix based on vowel harmony: -ıncı, -inci, -uncu, or -üncü. Because altı already ends in a vowel, we just add -ncı to get altıncı (sixth).

Why isn't the word for June (haziran) capitalized here?

In Turkish, names of months and days are only capitalized if they refer to a specific, exact date (for example, 15 Haziran). When talking about the month in general, like in this sentence, it is written in lowercase.

Where is the word for "is" in this sentence?

Turkish doesn't have a separate standalone word for "is". In simple statements like this, the "to be" suffix (-dır or -dir) is often completely left out. Saying Altıncı ay haziran is a complete sentence. You could technically say Altıncı ay hazirandır, but dropping the suffix is very common and natural here.

I learned that ay means "moon". Does it also mean "month"?

Exactly! The word ay means both "moon" and "month" in Turkish. Because this sentence is talking about June and the number six, the context clearly shows it means "month" here.