אנחנו יכולים להוכיח את התוצאה.

A word-by-word breakdown is:

• אנחנו = we
• יכולים = can / are able to (masculine plural)
• להוכיח = to prove
• את = marker of a definite direct object; it usually is not translated into English
• התוצאה = the result

So the whole sentence means We can prove the result.

Because it agrees with אנחנו (we).

In Hebrew, words like יכול / יכולה / יכולים / יכולות change to match the subject in gender and number:

• אני יכול = I can (male speaker)
• אני יכולה = I can (female speaker)
• אנחנו יכולים = we can (masculine or mixed group)
• אנחנו יכולות = we can (all-female group)

So אנחנו יכולים is the correct form if the group is male or mixed.

In Hebrew, can is often expressed with the word יכול plus an infinitive.

So instead of having a separate verb exactly like English can, Hebrew commonly uses a structure like:

• אני יכול ללמוד = I can study
• היא יכולה לבוא = She can come
• אנחנו יכולים להוכיח = We can prove

So יכולים behaves more like able in we are able to prove, even though in English we usually translate it as can.

להוכיח is the infinitive, meaning to prove.

The ל־ at the beginning is the normal infinitive marker in Hebrew, roughly like English to in to prove.

Examples:

• ללמוד = to study
• לעשות = to do / to make
• להוכיח = to prove

So after יכולים, Hebrew uses the infinitive:

• אנחנו יכולים להוכיח = we can prove

את marks a definite direct object.

In this sentence, the direct object is התוצאה (the result), and it is definite because it has ה־ (the). That is why Hebrew uses את before it:

• להוכיח את התוצאה = to prove the result

A very important point: את usually is not translated into English. It is just a grammatical marker.

Compare:

• אני רואה ילד = I see a boy
  
  • no את, because the object is indefinite
• אני רואה את הילד = I see the boy
  
  • את appears because the object is definite

Because the sentence is talking about the result, not just a result.

• תוצאה = a result
• התוצאה = the result

Since התוצאה is definite, Hebrew also adds את before it:

• להוכיח את התוצאה = to prove the result

If you said להוכיח תוצאה, that would sound like to prove a result, which is less natural in many contexts and also would not take את.

Yes. This is a very normal Hebrew word order:

subject + modal expression + infinitive + object

So:

• אנחנו = subject
• יכולים = can / are able
• להוכיח = to prove
• את התוצאה = the result

That gives:

• אנחנו יכולים להוכיח את התוצאה.

Hebrew word order can sometimes be flexible, but this is the most straightforward and neutral way to say it.

Sometimes yes, but it depends on style and context.

Hebrew often drops subject pronouns when the meaning is clear. So in context, someone might say:

• יכולים להוכיח את התוצאה. = We can prove the result.

However, keeping אנחנו is very natural, especially if you want to be clear or emphasize we.

So:

• אנחנו יכולים להוכיח את התוצאה = clear, neutral
• יכולים להוכיח את התוצאה = possible in context, more conversational

A simple pronunciation guide is:

Anachnu yekholim lehokhiakh et hatotsa'ah.

Approximate breakdown:

• אנחנו = a-NACH-nu
• יכולים = ye-kho-LIM
• להוכיח = le-ho-KHI-akh
• את = et
• התוצאה = ha-to-tsa-AH

A few notes:

• The ch/kh sound is the throaty Hebrew sound, like in German Bach or Scottish loch.
• The stress usually falls near the end in יכולים, להוכיח, and התוצאה.

The root is י־כ־ח.

להוכיח is a verb in the הפעיל (hif'il) pattern, which often has a causative sense, though you do not need to overthink that at first. In modern Hebrew, להוכיח simply means to prove.

Useful related forms:

• הוא הוכיח = he proved
• היא הוכיחה = she proved
• הוכחה = proof

So you can connect:

• להוכיח = to prove
• הוכחה = proof

Usually, yes, but the exact nuance depends on context.

תוצאה / התוצאה can mean:

• result
• outcome
• sometimes consequence

In a math or logic context, התוצאה is often best translated as the result. In another context, it might mean the outcome.

So in this sentence, We can prove the result is a good natural translation.

Then יכולים would become יכולות:

• אנחנו יכולות להוכיח את התוצאה.

Everything else stays the same.

So:

• אנחנו יכולים... = we can... (male or mixed group)
• אנחנו יכולות... = we can... (all-female group)

Yes. Hebrew has other ways to express possibility or ability.

For example:

• אפשר להוכיח את התוצאה. = It is possible to prove the result.
• אנחנו מסוגלים להוכיח את התוצאה. = We are capable of proving the result.

But אנחנו יכולים להוכיח את התוצאה is the most direct equivalent of We can prove the result.

So if you want the simplest, most natural match for the English sentence, the original version is excellent.