حقيبتي خلف الباب، وحقيبة صديقتي أمام الطاولة.

Because this is a nominal sentence in Arabic. In present-time statements, MSA usually leaves out the verb to be.

So:

حقيبتي خلف الباب
literally looks like
my bag behind the door

but it means:

My bag is behind the door.

The same thing happens in the second clause:

حقيبة صديقتي أمام الطاولة
= My friend’s bag is in front of the table.

The ending -ي means my.

So:

• حقيبة = a bag / bag
• حقيبتي = my bag

Also, when a noun ends in ة (taa marbuuTa), that ة becomes a pronounced ت when a suffix is attached.

So حقيبة is pronounced roughly ḥaqībah on its own, but حقيبتي is pronounced ḥaqībatī.

Because a noun with a possessive suffix is automatically definite.

So حقيبتي does not mean just a bag of mine in a vague way. It means the specific bag that belongs to me: my bag.

In Arabic, definiteness can come from:

• ال as in الباب = the door
• possession, as in حقيبتي = my bag

This is an iDaafa construction, often called the construct phrase.

Arabic usually expresses X of Y or possession by putting two nouns next to each other:

• حقيبة صديقتي
  literally: bag my-friend
  natural English: my friend’s bag / the bag of my friend

There is no separate word for of here.

The pattern is:

• thing possessed first: حقيبة
• owner second: صديقتي

Because in an iDaafa, the first noun normally does not take ال.

Its definiteness comes from the second noun.

Here, صديقتي is definite because it means my female friend, so the whole phrase حقيبة صديقتي is also definite:

the bag of my friend = my friend’s bag

So forms like الحقيبة صديقتي would be wrong in this structure.

صديقتي means my female friend.

Breakdown:

• صديقة = female friend
• -ي = my

So:

• صديقي = my male friend
• صديقتي = my female friend

This tells you the friend is female. It does not tell you whether the speaker is male or female.

For a learner, it is fine to think of them as words meaning:

• خلف = behind
• أمام = in front of

More precisely, traditional Arabic grammar often treats them as nouns/adverbs of place (ظروف مكان), not simple prepositions like في or على.

That is why they are followed directly by another noun:

• خلف الباب = behind the door
• أمام الطاولة = in front of the table

So in practice, they work a lot like prepositions in English, even though their grammar is a bit different.

Because they mean the door and the table.

So:

• الباب = the door
• الطاولة = the table

The sentence is talking about specific objects, not just any door or any table.

Also, after خلف and أمام, the following noun can be definite or indefinite depending on the meaning. Here it is definite.

In normal Arabic writing, short case endings are usually not written.

If fully vocalized, the sentence would be approximately:

حقيبتي خلفَ البابِ، وحقيبةُ صديقتي أمامَ الطاولةِ.

A few helpful notes:

• حقيبةُ صديقتي is the subject of the second clause, so حقيبةُ is nominative.
• خلفَ and أمامَ are commonly treated as adverbs of place, so they are accusative.
• البابِ and الطاولةِ are genitive after them.
• In forms like حقيبتي and صديقتي, the final case ending is not clearly visible because of the attached -ي.

Because Arabic does not need an extra word like it is in this kind of present-tense nominal sentence.

The structure is simply:

• noun phrase + location phrase

So:

• حقيبتي خلف الباب = My bag is behind the door
• حقيبة صديقتي أمام الطاولة = My friend’s bag is in front of the table

Using هي here would usually be unnecessary unless you wanted special emphasis.