Questa valigia non sta nel bagagliaio.

Because valigia is a feminine singular noun, and questo/quella-type words must agree with the noun.

• questo = masculine singular
• questa = feminine singular
• questi = masculine plural
• queste = feminine plural

So:

• questa valigia = this suitcase
• questo bagagliaio = this trunk

Sta is the third-person singular present form of stare.

Here the subject is questa valigia, which is singular, so the verb is singular too:

• io sto
• tu stai
• lui/lei sta
• noi stiamo
• voi state
• loro stanno

So questa valigia non sta... uses sta because the suitcase is one thing.

In Italian, stare can sometimes be used when talking about whether something fits or can be placed somewhere.

So in a sentence like this, non sta nel bagagliaio often means something like:

• it doesn’t fit in the trunk
• it won’t go in the trunk

That is different from non è nel bagagliaio, which simply says the suitcase is not in the trunk.

So stare here is about fitting/being able to be in that space, not just location.

That is the normal way to make a sentence negative in Italian:

• non + verb

Examples:

• non sta = does not fit / is not
• non mangio = I do not eat
• non capisce = he/she does not understand

So Questa valigia non sta nel bagagliaio follows the standard Italian negative pattern.

Nel is a contraction of:

• in + il = nel

So nel bagagliaio literally means in the trunk.

This is very common in Italian. Some similar combinations are:

• in + il = nel
• in + lo = nello
• in + la = nella
• in + i = nei
• in + gli = negli
• in + le = nelle

Because bagagliaio is a masculine singular noun, il is the article, so in il becomes nel.

Italian usually uses the definite article more often than English does.

So where English says in the trunk, Italian says nel bagagliaio.

Even when English might sometimes sound less article-heavy, Italian often still wants one. In this sentence, bagagliaio is not normally left bare, so in bagagliaio would sound wrong here.

Yes. That is also natural, but the nuance is slightly different.

• non sta nel bagagliaio = it doesn’t fit in the trunk
• non entra nel bagagliaio = it doesn’t go into the trunk / it won’t fit inside

Entrare focuses more on going into the space. Stare focuses more on being able to fit/be contained in the space.

In many everyday situations, both can work.

Yes. Bagagliaio is a masculine singular noun.

So you get:

• il bagagliaio
• nel bagagliaio
• questo bagagliaio

That masculine gender is the reason the article inside nel is il, not la.

A rough English-friendly pronunciation is:

ba-ga-LYA-yo

The tricky part is gli before a vowel. It is not exactly like normal English gl. It is a special Italian sound, similar to the lli sound in some pronunciations of Spanish ll.

Also:

• va-li-gia sounds roughly like va-LEE-ja
• bagagliaio has the stress on -glia-

So the full sentence is roughly:

KWES-ta va-LEE-ja non sta nel ba-ga-LYA-yo

That is only an approximation, but it helps get close.