אם תמצאי את הפותחן, נוכל לפתוח את הצנצנת.

Because תמצאי is the second-person feminine singular future form of למצוא (to find).

Hebrew marks gender in the second person, so this sentence is being said to one female.

Compare:

• אם תמצאי = if you (female) find
• אם תמצא = if you (male) find
• אם תמצאו = if you (plural) find

So the ending here tells you who is being addressed.

That is a very common difference between English and Hebrew.

In Hebrew, when the condition refers to the future, it is very normal to use the future tense after אם:

• אם תמצאי... נוכל...

In natural English, we usually use:

• If you find..., we can / will be able to...

So Hebrew and English do not match word-for-word here. Hebrew often uses future + future in this kind of sentence.

Here, את is the direct object marker. It does not have a meaning of its own in English, so it usually is not translated.

It appears before a definite direct object, usually one with ה- (the):

• את הפותחן = the opener
• את הצנצנת = the jar

This is one of the most important grammar words in Hebrew.

Also, learners often get confused because Hebrew has another word spelled את in unpointed text, meaning you (feminine singular). In this sentence, both instances are the object marker, not the pronoun.

Because they do different jobs:

• ה- makes the noun definite: the opener, the jar
• את marks that definite noun as the direct object of the verb

So:

• הפותחן = the opener
• את הפותחן = the opener, as a direct object

And similarly:

• הצנצנת = the jar
• את הצנצנת = the jar, as a direct object

A very useful rule is:

Use את before a direct object when that object is definite.

נוכל is the first-person plural future form meaning we will be able to or, in many contexts, simply we can.

So:

• נוכל לפתוח = we will be able to open / we can open

In English, the most natural translation may use can, but the Hebrew form itself is future.

Because after a verb of ability like נוכל, Hebrew normally uses the infinitive of the next verb.

So:

• נוכל לפתוח = we will be able to open

The ל- at the beginning of לפתוח is the normal infinitive marker, often similar to English to.

This is a standard pattern:

• אני רוצה לאכול = I want to eat
• הוא יכול לבוא = he can come
• נוכל לפתוח = we will be able to open

Because Hebrew usually does not need subject pronouns when the verb already shows the person, number, and sometimes gender.

Here:

• תמצאי already tells you you (feminine singular)
• נוכל already tells you we

So the sentence can leave the pronouns out naturally.

You could add them for emphasis:

• אם את תמצאי את הפותחן, אנחנו נוכל לפתוח את הצנצנת

But that is more emphatic than neutral.

Yes, in the sense of logic, but Hebrew does not need a separate word for it.

The structure is simply:

• אם X, Y = if X, then Y

So:

• אם תמצאי את הפותחן, נוכל לפתוח את הצנצנת means:
• If you find the opener, then we can open the jar

English also often leaves then out, so this works similarly.

They come from the same root: פ-ת-ח, which has to do with opening.

• לפתוח = to open
• פותחן = opener / opening tool

So the sentence repeats the same root in two related words:

• find the opener
• open the jar

That is very common in Hebrew. A learner can often recognize related words by spotting the same root.

It can mean both, depending on context.

In this sentence, it clearly means if, because it introduces a condition:

• אם תמצאי..., נוכל...

But in a sentence like:

• אני לא יודע אם היא בבית it means whether / if in the sense of an indirect question:
• I do not know whether she is at home

So the meaning of אם depends on how it is being used in the sentence.

It can be rearranged.

The given version is:

• אם תמצאי את הפותחן, נוכל לפתוח את הצנצנת.

But Hebrew can also say:

• נוכל לפתוח את הצנצנת אם תמצאי את הפותחן.

Both are natural. The original version puts the condition first, which is very common and easy to process.