Я хочу подчеркнуть, что это важное правило.

This is about verb aspect.

• подчеркнуть = perfective
• подчеркивать = imperfective

After хочу (I want), Russian can use either aspect depending on the meaning:

• Я хочу подчеркнуть = I want to make/emphasize this point as a single complete act.
• Я хочу подчеркивать = I want to keep emphasizing / emphasize repeatedly / be emphasizing.

In this sentence, the speaker means one clear act of emphasis, so подчеркнуть sounds natural.

Literally, подчеркнуть means to underline something in writing.

For example:

• подчеркнуть слово = to underline a word

But very often it is also used figuratively:

• подчеркнуть важность = to emphasize the importance
• Я хочу подчеркнуть... = I want to emphasize...

So in your sentence, it is the figurative meaning: to emphasize.

This is a very common Russian pattern:

• хотеть
  • infinitive

So:

• я хочу = I want
• подчеркнуть = to emphasize

Together:

• Я хочу подчеркнуть = I want to emphasize

This works just like English want + to + verb, except Russian uses the infinitive directly, without a separate word like to.

More examples:

• Я хочу знать. = I want to know.
• Мы хотим поговорить. = We want to talk.

Because что introduces a subordinate clause.

The sentence has two parts:

• Я хочу подчеркнуть
• что это важное правило

The second part depends on the first, so Russian puts a comma before что.

This is very standard:

• Я знаю, что он дома.
• Она сказала, что придёт.
• Мы видим, что это ошибка.

So the comma is required here.

Here что means that.

So:

• Я хочу подчеркнуть, что... = I want to emphasize that...

This is one of the most common uses of что in Russian.

Be careful: что can also mean what in other sentences, but not here.

For example:

• Что это? = What is this?
• Я знаю, что это важно. = I know that this is important.

Правило is in the nominative singular.

Here the phrase means:

• это важное правило = this is an important rule / it is an important rule

Russian often omits the present tense of to be. So there is no word for is in the sentence.

Literally, the structure is more like:

• это — важное правило

Both важное and правило match in:

• gender: neuter
• number: singular
• case: nominative

Because it has to agree with правило.

The noun правило is:

• neuter
• singular
• nominative

So the adjective must match it:

• важный = masculine
• важная = feminine
• важное = neuter
• важные = plural

Examples:

• важный вопрос = an important question
• важная книга = an important book
• важное правило = an important rule

So важное is the correct neuter form.

In this sentence, это can feel like either this or it, depending on how you translate it into natural English.

Russian это often points to something and identifies it:

• Это правило. = This is a rule. / It is a rule.
• Это важное правило. = This is an important rule.

So in your sentence:

• что это важное правило means
• that this is an important rule or more naturally in some contexts
• that it is an important rule

Russian uses это very often in this kind of identifying sentence.

Yes, Russian word order is flexible, but the original sentence is the most neutral and natural.

Original:

• Я хочу подчеркнуть, что это важное правило.

You could change the order for emphasis, for example:

• Я хочу подчеркнуть, что правило это важное.

But that sounds marked or stylistically unusual in many contexts.

Russian word order often changes to highlight different information, but for a learner, the safest choice is the standard order:

• это важное правило

Yes, sometimes.

Russian often drops the subject pronoun when it is clear from the verb ending.

• Я хочу подчеркнуть...
• Хочу подчеркнуть...

Both can mean I want to emphasize...

The version without Я can sound a bit more conversational or context-dependent. Including Я is clearer and often better for learners.

So:

• Я хочу подчеркнуть... = fully explicit
• Хочу подчеркнуть... = also natural, especially in speech

A rough pronunciation guide is:

• Я хочу́ подчеркну́ть, что э́то ва́жное пра́вило.

Approximate English-style help:

• ya kha-CHOO pat-char-KNOOT', shto EH-ta VAZH-na-ye PRA-vee-la

A few useful pronunciation notes:

• что is usually pronounced more like што, not a careful ч-to
• о often sounds closer to a when unstressed
• ь in подчеркнуть softens the final consonant

If you want to sound natural, the main stresses are:

• хочу́
• подчеркну́ть
• э́то
• ва́жное
• пра́вило