kaeri no densya de tonari no onnanoko ni hanasikakerarete, kondo eiga ya dorama no hanasi wo siyou to sasowareta.

帰り is a noun here, not a verb. It means the way back, the return trip, or often the way home.

So:

• 帰りの電車 = the train on the way back
• in natural English, often the train ride home or the train on the way home

The の connects 帰り to 電車, so 帰り works like a modifier:

• 帰り = return
• 帰りの電車 = return-train / train for the return trip

This is a very common pattern in Japanese.

Here, で marks the place or setting where the action happened.

So:

• 電車で = on the train / in the train

Even though で can also mean by means of, in this sentence it is best understood as the location of the event:

• the speaker was spoken to on the train

隣 means next to, neighboring, or adjacent.

So:

• 隣の女の子 = the girl next to me / the girl beside me

Literally, it is something like the neighboring girl, but in natural English it means the girl sitting or standing next to the speaker.

The person being next to someone is understood from context. Here, it is most naturally the girl next to the speaker.

In a passive sentence, に often marks the person who performed the action.

So in:

• 隣の女の子に話しかけられて

the girl next to me is the one who did the action of speaking.

A helpful comparison:

• Active: 隣の女の子が私に話しかけた
  = The girl next to me spoke to me.
• Passive: 私は隣の女の子に話しかけられた
  = I was spoken to by the girl next to me.

So に marks the doer in the passive version.

話しかけられて is the て-form of the passive of 話しかける.

• 話しかける = to speak to someone / to start talking to someone
• 話しかけられる = to be spoken to
• 話しかけられて = being spoken to, and then...

Japanese often uses the passive when the speaker is the one affected by someone else’s action. In English, we might simply say a girl next to me started talking to me, but Japanese commonly says it from the speaker’s side as I was spoken to.

This does not have to sound negative. It can just mean:

• someone unexpectedly addressed me
• I was approached / spoken to

The て-form links this action to the next one.

So the sentence structure is basically:

• 話しかけられて、誘われた
• I was spoken to, and then I was invited

It connects the events in sequence. A natural English rendering would be:

• I was spoken to by the girl next to me on the train home, and then she invited me...

So 話しかけられて sets up the first event before the second event 誘われた.

Here, 今度 means next time, sometime soon, or on another occasion.

So:

• 今度 映画やドラマの話をしよう
  = Let’s talk about movies and dramas sometime / next time

Be careful: 今度 can sometimes mean this time in other contexts. But in this sentence, because it is part of an invitation, it clearly means something like next time or sometime soon.

や is used to list examples in a non-exhaustive way.

So:

• 映画やドラマ = movies, dramas, and things like that

It is different from a strict and. It suggests examples rather than a complete list.

Compare:

• 映画とドラマ = movies and dramas
• 映画やドラマ = movies, dramas, etc.

So the speaker is not necessarily limiting the topic to only those two things.

話 means talk, conversation, or discussion.

So:

• 映画やドラマの話 = talk about movies and dramas
• more naturally: a conversation about movies and TV dramas

The の links the topic to 話:

• Aの話 = talk/story/discussion about A

This is a very common pattern:

• 仕事の話 = talk about work
• 旅行の話 = talk about travel
• 映画の話 = talk about movies

しよう is the volitional form of する.

• する = do
• しよう = let’s do / shall we do

So:

• 話をしよう = let’s talk

In this sentence, the girl is inviting the speaker, so the volitional form makes perfect sense. It expresses a suggestion or invitation.

Here, と marks the content of the invitation, like a quotation or quoted idea.

So:

• 話をしようと誘われた
  = I was invited with the idea, Let’s talk = more naturally, I was invited to talk

You can think of it as connecting the proposed action to 誘う:

• 〜しようと誘う = to invite someone to do ~

So the content of the invitation is:

• 今度 映画やドラマの話をしよう
• let’s talk about movies and dramas sometime

Just like 話しかけられて, this is another passive form centered on the speaker.

• 誘う = to invite
• 誘われる = to be invited
• 誘われた = was invited

Japanese often tells the story from the point of view of the person receiving the action:

• I was spoken to
• I was invited

That is why both verbs are passive. It keeps the speaker as the understood subject throughout the sentence.

The subject is omitted, but it is understood to be I or me.

Japanese often leaves out subjects when they are clear from context. Here, the passive forms strongly suggest that the speaker is the one affected:

• 話しかけられて = I was spoken to
• 誘われた = I was invited

So even without 私, the sentence naturally reads as a first-person experience.

Not necessarily. 女の子 literally means girl, but in real Japanese it can sometimes be used more loosely for a young female person, depending on the speaker and situation.

So in context, it could mean:

• a girl
• a young woman
• a younger female passenger

A translation may choose girl because that is the literal word, but the exact age range depends on context.

Not automatically. Japanese passive can sometimes have an affected nuance, meaning the speaker is presenting the event from the standpoint of being on the receiving end of it. But that does not always mean the event was bad.

In this sentence, the passive can suggest things like:

• the speaker was unexpectedly approached
• the action happened to the speaker
• the narration is centered on the speaker’s experience

Because the second half is an invitation to talk about movies and dramas, the overall tone does not sound especially negative. It is more like:

• A girl next to me started talking to me, and then invited me to talk about movies and dramas sometime.

Yes. For example:

• 帰りの電車で隣の女の子が私に話しかけてきて、今度映画やドラマの話をしようと私を誘った。

That would mean roughly:

• On the train home, the girl next to me started talking to me and invited me to talk about movies and dramas sometime.

The original sentence, though, is more natural if the speaker wants to keep the focus on their own experience:

• I was spoken to
• I was invited