Learn Hardcore Chinese: wǒ xīwàng wǒmen kěyǐ yìqǐ jiějué zhè gè wèntí. - I hope we can solve this problem together.

希望 = to hope, to wish
- Often used when the result depends on factors beyond your direct control.
- Sounds a bit more formal and emotional.
- 我希望我们可以一起解决这个问题。
  → You’re expressing a hope; it may or may not happen.
想 = to think / to want (to do something)
- More about your internal intention or idea.
- If you say 我想我们可以一起解决这个问题, it’s more like “I think we can solve this problem together” (an opinion/judgment), not “I hope...”.
要 = to want / to be going to / must
- More forceful or determined.
- 我要解决这个问题 sounds like “I’m going to / I must solve this problem.”

So 希望 is the natural choice when you’re politely and emotionally expressing a hope about the future outcome, as in the given sentence.

In English we say “I hope that we can…”. Why is there no word for “that” between 希望 and 我们?

In Chinese, you usually don’t need a separate word for English “that” when introducing a clause after verbs like 希望, 觉得, 认为, 知道, etc.

So:

English: I hope that we can solve this problem together.
Chinese: 我希望我们可以一起解决这个问题。
(literally: I hope we can together solve this problem.)

You could add a “that”-like connector such as 希望（能）……, but you still wouldn’t use a word that directly corresponds to English that. The clause 我们可以一起解决这个问题 just directly follows 希望.

What is the difference between 可以 (kěyǐ) and 能 (néng) here? Could I say 我希望我们能一起解决这个问题 instead?

Both work, but they have slightly different focuses:

可以 emphasizes permission / possibility.
- It often implies “be allowed to / be able to (under certain conditions)”.
- 我希望我们可以一起解决这个问题。
  → “I hope we can / are able to solve this problem together” (it’s possible / permitted).
能 emphasizes ability / capability or realistic possibility.
- 我希望我们能一起解决这个问题。
  → “I hope we are able to / manage to solve this problem together.”

In this sentence, 可以 and 能 are both natural and common.
If you really want to distinguish:

可以: Slightly more about the situation allowing it.
能: Slightly more about us being able to pull it off.

But in everyday speech, the difference here is usually very subtle.

Can I just drop 可以 and say 我希望我们一起解决这个问题? Does it change the meaning?

Yes, you can say:

我希望我们一起解决这个问题。

The meaning is still “I hope we solve this problem together,” but:

With 可以 / 能:
→ Emphasizes possibility or ability:
我希望我们可以/能一起解决这个问题。
Without 可以 / 能:
→ Sounds a bit more direct: “I hope we (will) solve this problem together.”

In many contexts, all three versions (with 可以, with 能, or without any modal) are acceptable, and the difference is more about nuance than basic meaning.

Why is 一起 (yìqǐ) placed before 解决 (jiějué)? Can I move it somewhere else?

The standard and most natural order is:

一起 + 动词 (verb)
→ 一起解决 = “solve together”

In your sentence:

我们可以一起解决这个问题。

Alternative positions:

我们一起可以解决这个问题。
- Grammatically possible, but the focus shifts very slightly onto 可以解决 (“are able to solve”). Still acceptable.
一起我们可以解决这个问题。
- This is unnatural in Chinese.

So, the default and best choice is exactly what you have:
我们可以一起解决这个问题。

What exactly does 解决 (jiějué) mean? How is it different from 处理 (chǔlǐ) or 解决办法 (jiějué bànfǎ)?

解决 = to solve; to resolve
- Emphasizes reaching a resolution so that the problem is essentially gone.
- 解决问题 = “solve a problem”.
处理 = to handle; to deal with
- Focuses on taking action, not necessarily fully solving it.
- 处理问题 = “deal with a problem” (may or may not be fully resolved).
解决办法 = solution / way to solve (lit. “solve-method”)
- 办法 = method / way.
- 找到解决这个问题的办法 = “find a way to solve this problem”.

In your sentence, you want “solve this problem”, so 解决这个问题 is exactly right.

Why do we need 个 (gè) between 这 (zhè) and 问题 (wèntí)? Can we just say 这问题?

个 here is a measure word (classifier). In Chinese, when you use a demonstrative like 这 (this) with a noun, you normally also need a measure word:

这 + 个 + 问题 = “this (one) problem”

So:

这个问题 is the standard form.
这问题 can occur in some very casual or dialect-influenced speech, but it’s not standard and is less common in proper Mandarin.

个 is the default, very general measure word, and 问题 commonly uses 个:

一个问题, 这个问题, 那个问题, 每个问题, etc.

That’s why 这个问题 is used, not just 这问题.

Why is 这 (zhè) needed at all? Could I just say 我希望我们可以一起解决问题?

Yes, you can say:

我希望我们可以一起解决问题。

The difference:

解决这个问题 = solve this (specific) problem
- Refers to a particular problem that both speakers know about.
解决问题 = solve problems / solve the problem(s) (more general)
- Could mean the currently discussed issue in a less specific way, or problems in general.

In contexts where both people clearly know which problem is being discussed, 解决问题 is still understood as solve the problem, but 这个 makes it sound more specific and pointed.

How do we know this sentence is about the future? There is no tense marker like “will”.

Chinese doesn’t have verb tense in the same way English does. Time is usually understood from:

Context (what you’re talking about)
Time words (明天, 以后, 现在, etc.)
The kind of verb used (like 希望, 打算, 要, etc.)

Here, 希望 (to hope) naturally suggests a situation that has not yet happened:

我希望我们可以一起解决这个问题。
→ By default, it means “I hope we will solve this problem together (in the future).”

If you want to make the future even clearer, you can add a time word:

我希望以后我们可以一起解决这个问题。
我希望明天我们可以一起解决这个问题。

Can I drop 我 (wǒ) and just say 希望我们可以一起解决这个问题?

Yes, in contextual, informal speech or writing, it is possible to drop 我:

希望我们可以一起解决这个问题。

This often happens:

In group messages or announcements, where the speaker is obvious.
When the sentence appears after another sentence that already made the subject clear.

However, if the sentence stands alone (for example, as the first sentence in an email), including 我 is clearer and more natural:

我希望我们可以一起解决这个问题。

In English, “we” can be inclusive (“you and I”) or exclusive (“my group but not you”). Does 我们 (wǒmen) distinguish these?

No. 我们 does not grammatically distinguish inclusive vs. exclusive “we”.

我们 can mean:
- “you and I / all of us including you”
- “we (but not you)”

Which one it is depends entirely on context.

In this sentence:

我希望我们可以一起解决这个问题。

Most naturally, 我们 is inclusive (“you and I together”), because of 一起 (together) and the cooperative context of solving a problem.

Is this sentence formal or informal? Would it be appropriate in an email to a colleague or boss?

我希望我们可以一起解决这个问题。 is polite and neutral, appropriate in many contexts:

Spoken or written
To friends, colleagues, superiors, or customers

If you want it to sound a bit more formal or written, you might see variants like:

我希望我们能一起解决这个问题。
我希望我们可以共同解决这个问题。 (共同 is a bit more formal than 一起.)

But the original sentence is already fine for a professional email, especially if the overall tone of the email is polite.