Если я знаю причину проблемы, я могу решить её.

Если means if.

This sentence uses the present tense in both parts:

• я знаю = I know
• я могу решить = I can solve

In Russian, that is very normal for a general real condition:

• Если я знаю причину проблемы, я могу решить её.
• If I know the cause of the problem, I can solve it.

Russian does not need a special future or conditional form here the way English sometimes does in grammar explanations.

Знаю is the 1st person singular present tense of знать:

• знать = to know
• я знаю = I know

So the subject я and the verb знаю match:

• я знаю
• ты знаешь
• он/она знает

A learner might expect just the dictionary form, but Russian normally uses a fully conjugated verb, just like English uses I know, not I to know.

Because причину is the accusative case of причина.

The verb знать usually takes a direct object, and direct objects often go in the accusative:

• причина = nominative
• причину = accusative

So:

• Я знаю причину = I know the cause/reason

This is the same basic idea as in:

• Я знаю ответ. = I know the answer.
• Я вижу машину. = I see a car.

Because проблемы here means of the problem.

The phrase is:

• причина проблемы = the cause of the problem

In Russian, this of relationship is usually shown with the genitive case, not with a separate word like English of.

So:

• проблема = problem
• проблемы = of the problem

Together:

• причину проблемы = the cause of the problem

The whole phrase is built like this:

• причину = accusative, because it is the direct object of знаю
• проблемы = genitive, because it depends on причина

Because the first part of the sentence is a subordinate clause introduced by если.

Russian normally puts a comma before the main clause in sentences like this:

• Если ..., ...

So:

• Если я знаю причину проблемы, я могу решить её.

This comma is required in standard written Russian.

Compare:

• Когда я приду, мы начнём.
• Потому что я устал, я ушёл.

Russian uses commas with these clause linkers more consistently than English does.

Because могу решить means can solve or am able to solve.

• могу = I can
• решить = to solve / to resolve

So:

• я могу решить её = I can solve it

If you said я решаю её, that would usually mean I am solving it or I solve it, which is a different idea.

The original sentence is about ability or possibility, not about the action already being in progress.

This is about aspect, one of the biggest grammar topics in Russian.

• решать = imperfective
• решить = perfective

Very roughly:

• решать focuses on the process, repetition, or ongoing action
• решить focuses on reaching the result: the problem gets solved

In this sentence, the meaning is that knowing the cause lets you solve the problem successfully, so решить is natural.

Compare:

• Я могу решать такие задачи. = I can solve this kind of problem / I know how to handle such tasks
  More about general ability or process.

• Я могу решить эту проблему. = I can solve this problem.
  More about a specific successful outcome.

Её means it here, and it refers to проблему.

Even though the noun проблема appears inside причину проблемы, it is still clear that the speaker means:

• решить её = solve it
• it = the problem

Why её?

Because проблема is a feminine noun, and in the accusative singular the pronoun is:

• её = her / it

So:

• решить её = solve it

Yes, often it can.

Russian sometimes leaves out an object if it is obvious from context. So both of these are possible:

• Если я знаю причину проблемы, я могу решить её.
• Если я знаю причину проблемы, я могу решить.

However, the version with её is clearer and sounds more complete on its own.

Without context, решить by itself can sound slightly open-ended, as if the listener might ask, Solve what?

So in an isolated teaching sentence, её is a helpful choice.

Yes. Russian word order is more flexible than English word order.

The original sentence is neutral and clear:

• Если я знаю причину проблемы, я могу решить её.

But you could also say:

• Я могу решить её, если я знаю причину проблемы.
• Если причину проблемы я знаю, я могу решить её.

These versions may change the emphasis a little, but the core meaning stays the same.

Russian often uses word order to highlight what is new, important, or contrasted, not just to mark grammar.

It can be either, depending on context.

• причина = reason or cause

In a sentence about a problem, cause often sounds more natural in English:

• the cause of the problem

But in many situations, reason is also possible.

Russian причина covers both ideas more broadly than English sometimes does, so the best translation depends on what sounds most natural in context.

In careful pronunciation, её is pronounced roughly like yi-YO.

A few useful points:

• the stress is on the second syllable
• the ё sound is always stressed
• in normal writing, Russian often writes её correctly with ё, though in many words ё is often replaced by е

So:

• её = roughly yi-YO

This is important because её is not pronounced like the letters might suggest to an English speaker if read one by one.

Yes, absolutely.

• причину проблемы = the cause of the problem
• причину этой проблемы = the cause of this problem

Adding этой makes it more specific.

Both are correct:

• Если я знаю причину проблемы, я могу решить её.
• Если я знаю причину этой проблемы, я могу решить её.

The second version points more clearly to one particular problem already being discussed.