wǒmen děi xiǎng yí gè bànfǎ jiějué zhè gè wèntí.

Here 得 means must, have to, or need to. So 我们得想一个办法 means we need to think of a way.

This is a different 得 from the very common grammar particle pronounced de or dé. Mandarin has several words written 得, so learners often have to tell them apart by context:

• děi = must / have to
• de = a grammatical particle, as in 跑得快
• dé = to get / obtain, in some words and expressions

In this sentence, it is clearly the modal verb děi.

This is because of a very common tone change rule for 一.

Normally, 一 is first tone (yī), but:

• before a fourth-tone syllable, it changes to second tone: yí
• before a non-fourth-tone syllable, it usually changes to fourth tone: yì

Here it comes before 个 gè, which is fourth tone, so 一 个 is pronounced yí gè.

They do two different jobs, even though they are the same measure word.

• 一 个 办法 = one method / a way
• 这 个 问题 = this problem

In Mandarin, nouns often need a measure word after numbers and demonstratives:

• 一 + measure word + noun
• 这 / 那 + measure word + noun

So 个 is required in both places.

Here 想 means to think of, to come up with, or to consider. It does not mean want in this sentence.

想 can mean different things depending on context:

• 我想你。 = I miss you / I’m thinking about you.
• 我想喝咖啡。 = I want to drink coffee.
• 想一个办法。 = think of a way / come up with a solution.

So in 我们得想一个办法, the meaning is we need to come up with a way.

The structure is:

• 我们 = subject
• 得 = must / need to
• 想一个办法 = think of a way
• 解决这个问题 = solve this problem

So the whole sentence means something like:

We need to think of a way to solve this problem.

Chinese often puts actions one after another without needing an extra word like to. So 想一个办法解决这个问题 is literally more like:

think of a way, solve this problem

but the natural meaning is think of a way to solve this problem.

Yes, semantically it tells you what kind of 办法 is needed: a way to solve this problem.

However, it is not written as a full relative clause with 的, like 解决这个问题的办法. Instead, this sentence uses a more flowing verbal structure:

• 想一个办法解决这个问题

This is very natural in Chinese. You can understand it as:

• think of a method, and use it to solve this problem
• or more naturally, think of a method to solve this problem

Yes, absolutely. 想办法解决这个问题 is very common and natural.

The difference is:

• 想办法 = think of a way / figure something out
• 想一个办法 = think of one specific way / come up with a particular method

So 一个 makes it a little more concrete, but both are correct.

Both can mean method or way, but 办法 often sounds more like a practical solution to a problem.

• 办法 = a workable way, a solution, something you can do
• 方法 = method, technique, approach

In this sentence, 办法 fits very well because the speaker is dealing with a problem and needs a solution.

For example:

• 我有一个办法。 = I have an idea / I have a solution.
• 这个学习方法很好。 = This study method is very good.

Chinese often does not need a separate marker for infinitives like English to.

English says:

• a way to solve this problem

Chinese can simply say:

• 一个办法解决这个问题

The relationship is understood from context and word order. Chinese frequently links verbs directly in this way, especially when one action leads to or supports another.

Yes, that is also correct and natural.

Adding 来 makes the purpose relationship a little more explicit:

• 想一个办法解决这个问题 = think of a way to solve this problem
• 想一个办法来解决这个问题 = think of a way in order to solve this problem

The version without 来 is already perfectly normal, so you do not need 来, but you can use it.

Yes, if the subject is already clear from context, Chinese often omits it.

So depending on the situation, a speaker might simply say:

• 得想一个办法解决这个问题。

That would still mean We need to think of a way to solve this problem or We’ve got to figure out a way to solve this problem.

Chinese often drops subjects when they are understood.

Yes. The sentence follows a very common pattern:

subject + modal verb + main action + object + second action + object

So:

• 我们 = subject
• 得 = modal verb
• 想一个办法 = first action
• 解决这个问题 = second action

This kind of action chaining is very common in Mandarin. Once you get used to it, sentences like this feel very natural.