Ad sinistram taberna est, ad dextram autem bibliotheca.

Because they follow ad, and ad takes the accusative case.

In this sentence, ad sinistram and ad dextram mean on the left and on the right more literally to the left side and to the right side. Latin often uses ad + accusative for position in expressions like this.

So:

• sinistra = left side
• dextra = right side
• ad sinistram = to/on the left
• ad dextram = to/on the right

Even though English uses on, Latin uses ad here.

They are feminine because they come from feminine nouns:

• sinistra, -ae = left hand / left side
• dextra, -ae = right hand / right side

In this sentence, the words are being used almost like shortened expressions for the left side and the right side, so they stay feminine.

Their forms are:

• sinistram = accusative singular feminine
• dextram = accusative singular feminine

That matches what ad requires.

Because they are the subjects of the sentence.

The verb est means is, and the thing that is somewhere goes in the nominative case. So:

• taberna est = the shop is
• bibliotheca = the library (understood with est)

The location phrases ad sinistram and ad dextram tell you where the subjects are, but the subjects themselves stay nominative.

Because Latin often leaves out a verb when it is easily understood from the previous part of the sentence.

So:

• Ad sinistram taberna est
• ad dextram autem bibliotheca

really means:

• Ad sinistram taberna est, ad dextram autem bibliotheca est.

The second est is omitted because it would be obvious. This is very common in Latin.

Autem usually means however, but, or on the other hand.

Here it marks a contrast between the two sides:

• on the left, there is a shop
• on the right, however, a library

It is a very common Latin connective. One important thing to notice is that autem is often placed second in its clause, not necessarily first. So ad dextram autem bibliotheca is normal Latin word order.

Latin word order is more flexible than English word order because Latin uses case endings to show grammatical function.

English depends heavily on word order:

• The shop is on the left

Latin can move elements around more freely:

• Ad sinistram taberna est
• Taberna ad sinistram est

Both are possible. The chosen order often emphasizes what comes first. Here, the sentence begins with the locations ad sinistram and ad dextram, which helps set up a left-versus-right contrast.

Literally, it is closer to to the left. But in context it often simply means on the left or to the left-hand side.

This is a good example of where Latin and English do not match word-for-word. You should understand the phrase idiomatically rather than too literally.

So in practice:

• ad sinistram = on the left / to the left
• ad dextram = on the right / to the right

Yes.

For left, Latin can use:

• sinister, sinistra, sinistrum
• laevus, laeva, laevum

For right, Latin often uses:

• dexter, dextra, dextrum

In this sentence, sinistram and dextram are very natural. A learner should just note that Latin sometimes has more than one common word for the same basic idea.

Because Latin does not need a separate dummy word like English there.

English says:

• There is a shop

But Latin simply says:

• taberna est = a shop is

When Latin wants to say that something exists or is somewhere, it often just uses esse without any equivalent of English there.

So Ad sinistram taberna est is a normal way to express There is a shop on the left.

It is a Greek borrowing that became a normal Latin word.

• bibliotheca originally comes from Greek
• in Latin it means library or book-room

This is very common in Latin, especially for cultural or learned vocabulary. Even if a word was borrowed, once it is used in Latin, it behaves like a normal Latin noun. Here bibliotheca is a first-declension feminine nominative singular.

You know from the context and from the verb.

The verb here is est = is, which describes state/location, not movement. So the phrases are understood as telling where something is located.

If the sentence had a verb of motion, such as it (goes) or currit (runs), then ad + accusative would much more clearly suggest movement toward something.

So grammar gives one clue, but the verb and overall meaning are also important. Here the sense is clearly positional:

• the shop is on the left
• the library is on the right