wǒ zài zhè gè chéngshì zhù le liù gè yuè le.

Chinese teachers often call them verb 了 and sentence-final 了:

• The first 了 (right after 住) is verb 了.

  • Pattern: 住了六个月
  • It marks the completion/realization of a duration: “lived for six months (this stretch of time has been reached).”

• The second 了 at the end of the sentence is sentence-final 了.

  • Pattern: …六个月了。
  • It marks a change of situation / new state: “Now, as of this moment, it has (already) been six months.”

Together, 住了六个月了 means:

• “I have (already) lived in this city for six months (up to now, and I’m still here).”

In normal contexts, 我在这个城市住了六个月了 strongly suggests:

• You started living here six months ago,
• And you are still living here now.

That sense of “up to now and still true” comes mainly from:

• The duration (六个月)
• Plus the sentence-final 了.

If you wanted to clearly say you used to live in this city for six months but don’t anymore, you’d usually say something like:

• 我以前在这个城市住了六个月。
  (“I used to live in this city for six months.”)

Very roughly:

• 我在这个城市住了六个月了

  • Feels like “I have been living in this city for six months (already)”
  • Implies it’s still true now, and the speaker is aware of the time that has passed.

• 我在这个城市住了六个月 (no final 了)

  • Neutral description: “I lived / have lived in this city for six months.”
  • Often sounds more like a completed past period, and by itself does not clearly say whether you still live there.

Context can blur this difference, but in beginner–intermediate learning, a common rule of thumb is:

• Duration + verb 了 + sentence-final 了 = still true now.

You have two common patterns:

1. 在 + place + verb

   • 我在这个城市住了六个月了。
     Literally: “I at this city lived six months already.”

2. verb + 在 + place

   • 我住在这个城市已经六个月了。
   • 我已经住在这个城市六个月了。

Your version 我住在这个城市六个月了 is grammatical, but:

• It’s more natural if you also add 已经 or 了 after the verb:
  
  • 我已经住在这个城市六个月了。

So:

• 在 + 地方 + 住… and 住在 + 地方… are both correct structures, just slightly different word orders:
  • 我在上海住。
  • 我住在上海。

在 (zài) here is a location marker. The pattern is:

• [Subject] + 在 + [place] + [verb]

So in 我在这个城市住了六个月了:

• 在这个城市 = “in this city” (location)
• 住 = “live”

It’s similar to English “live in this city”, but in Chinese:

• The preposition-like word 在 comes before the place phrase:
  • 在这个城市 = “in this city”
  • Not “这个城市在”.

You can either:

• Put 在 + place before the verb: 我在这个城市住…
• Or fold 在 into the verb as 住在: 我住在这个城市…

There are two 个 here, doing two different jobs:

1. 这 + 个 + 城市

   • 个 is the measure word (classifier) for 城市 (city).
   • Many nouns need a measure word when counted or specified:
     
     • 一个人 (one person)
     • 三个苹果 (three apples)
     • 这个城市 (this city)

2. 六 + 个 + 月

   • Here 个 is the measure word for a period of a month.
   • 六个月 = “six months (of time).”

Why not 六月?

• 六月 (no 个) usually means “June” (the sixth month of the year), not “six months.”
• When you mean a span of time, you say:
  • 一个月 (one month)
  • 两个月 (two months)
  • 六个月 (six months)

Standard word order for location is:

• [Subject] + 在 + [place] + [verb] + …

So:

• 我在这个城市住了六个月了。

You can also:

• Use 住在 and move the place:
  • 我住在这个城市已经六个月了。
• Add time words like 已经 in different places:
  • 我已经在这个城市住了六个月了。
  • 我在这个城市已经住了六个月了。

But you cannot normally separate 在 from its place or put it far from the verb in strange ways. Patterns like:

• ✗ 我住了在这个城市六个月了 (wrong)
• ✗ 我在住这个城市六个月了 (wrong)

are ungrammatical.

To emphasize past, no longer true:

• 我以前在这个城市住了六个月。
  “I used to live in this city for six months.”
• 我在这个城市住了六个月，后来搬走了。
  “I lived in this city for six months, then moved away.”

To emphasize up to now and still true:

• 我在这个城市住了六个月了。
• 我已经在这个城市住了六个月了。

These are close to English:

• “I have lived / have been living in this city for six months (now).”

For the future, you usually don’t use this double-了 pattern. Instead, use a future marker or intent verb:

• 我要在这个城市住六个月。
  “I’m going to live in this city for six months.”
• 我会在这个城市住六个月。
  “I will live in this city for six months.”
• 打算在这个城市住六个月。
  “(I) plan to live in this city for six months.”

Key points:

• No 了 is needed for a simple future duration statement.
• 要 / 会 / 打算 show future intent or prediction.

• Replacing the final 了 with 呢:

  • 我在这个城市住了六个月呢 is not a standard way to express duration up to now.
  • 呢 is more for ongoing actions / states or soft questions, not for this particular “up to now” duration pattern.

• Leaving out the final 了:

  • 我在这个城市住了六个月 is grammatically fine.
  • But it’s less clear that you are still living here; it often sounds like a completed past period.

So:

• For “I’ve already been here six months (and I’m still here)”, keep the final 了:
  
  • …住了六个月了。

By itself, …住了六个月了 is neutral, but:

• The final 了 + duration tends to highlight that the time is not short / feels significant.
• Depending on tone of voice and context, it can carry different shades:
  • Mild surprise:
    
    • “Wow, it’s already been six months.”
  • Mild complaint or impatience:
    
    • “I’ve been stuck here six months already…”
  • Simple statement of fact:
    
    • “I’ve been here six months now.”

So grammatically it’s neutral; the emotion comes from context and intonation.

Some common casual variants:

• 我在这儿住了六个月了。
  (“this city” → “here”)
• 我在这儿住六个月了。
  (often the first 了 is dropped in fast speech)
• 我在这边住了半年了。
  (半年 = “half a year”)
• 我在这儿都住了六个月了。
  Adding 都 gives emphasis: “I’ve already been here six whole months.”

All of these still keep the core pattern:

• 在 + place + 住 + (了) + duration + 了 to express “(have been) living here for X time (up to now).”