Puella cupit cum amica sua ad thermas ire.

Because cupit (she wants/desires) is a verb that commonly takes an infinitive to complete its meaning: cupit ire = wants to go.
So the structure is:

• Puella cupit = The girl wants
• ire = to go (what she wants to do)

Latin often uses an infinitive where English uses to + verb.

In this sentence, puella is the subject of cupit, and the infinitive ire is understood to share the same subject unless something else is specified.
So it means: The girl wants (herself) to go.

If Latin wanted to say she wants her friend to go, it would normally use an accusative + infinitive pattern, e.g. puella cupit amicam ire = the girl wants the friend to go.

Puella is nominative singular, so it’s the subject: the girl.
The ending -a is a common nominative singular ending for 1st-declension nouns.

Cupit is present tense, 3rd person singular: (she/he/it) wants.
It comes from cupere (to desire, want). The -it ending marks 3rd singular present for many verbs.

Because cum (with) takes the ablative case.
So:

• amica = ablative singular (with a friend)
• amicam would be accusative singular, which is not used after cum.

Sua is the reflexive possessive adjective meaning her own (referring back to the subject puella).
So cum amica sua means with her (own) friend—i.e., the girl’s friend.

Eius would mean his/her but typically refers to someone else’s (not the subject’s) in contexts like this. For example, it could suggest with his/her friend (someone else’s friend) depending on context.

Both are ablative singular feminine:

• amica: ablative singular (after cum)
• sua: agrees with amica in gender (feminine), number (singular), and case (ablative)

Latin adjectives (including possessives) match the noun they describe.

Ad takes the accusative to show motion toward a destination.
So thermas is accusative plural.

The plural is normal because thermae (baths / bathhouse) is commonly used as a plural-only (or usually plural) noun in Latin, similar to English baths in the sense of a bathing complex.

They express different ideas:

• ad thermas = to/toward the baths (motion, destination)
• in thermis = in/at the baths (location)

So this sentence focuses on going to the baths, not already being there.

Latin word order is fairly flexible because endings show grammatical roles. You could rearrange many parts without changing the basic meaning, e.g.:

• Puella cupit ire ad thermas cum amica sua.
• Cum amica sua puella ad thermas ire cupit.

However, word order can affect emphasis. Placing something earlier often highlights it.

It’s a stylistic choice. Latin often places phrases where they read smoothly or where the writer wants emphasis. Putting cum amica sua before ad thermas ire can make with her friend feel like part of the plan before stating the destination and action.

Many learners also see cum + ablative phrases placed near what they modify, but Latin isn’t strict about it.