מכונת התפירה יכולה לתפור את הבד.

A common pronunciation is:

Mekhonat hatfirá yekholá litfór et habád.

A rough syllable breakdown:

• מכונת — me-kho-nat
• התפירה — ha-tfi-ra
• יכולה — ye-kho-la
• לתפור — lit-for
• את — et
• הבד — ha-bad

Because this is a construct phrase in Hebrew, called סמיכות.

The basic noun is מכונה = machine.
When it is followed by another noun to mean something like X of Y or an English compound noun, it often changes form:

• מכונה = machine
• מכונת = machine of ...

So:

• מכונת תפירה = a sewing machine
• literally: machine of sewing

This is very common in Hebrew.

In a construct phrase, the definiteness of the whole phrase is usually shown on the second noun, not the first.

So:

• מכונת תפירה = a sewing machine
• מכונת התפירה = the sewing machine

Even though מכונת itself does not have ה, the whole phrase is definite because התפירה is definite.

תפירה is the noun sewing.
So מכונת תפירה literally means machine of sewing.

English often uses noun compounds like sewing machine, but Hebrew commonly builds the same idea with a construct chain.

Also, תפירה and לתפור are related:

• תפירה = sewing
• לתפור = to sew

They come from the same root: ת־פ־ר.

Because מכונת התפירה is grammatically feminine singular.

The word יכול changes to match the gender and number of the subject:

• יכול = masculine singular
• יכולה = feminine singular
• יכולים = masculine plural
• יכולות = feminine plural

Since מכונה is feminine, the sentence needs יכולה.

Yes, in this sentence it functions like can / is able to.

More literally, יכולה means able in the feminine singular form. Hebrew often expresses ability with a form of יכול plus an infinitive:

• היא יכולה לתפור = she can sew
• מכונת התפירה יכולה לתפור = the sewing machine can sew

So it is very natural Hebrew, even though the structure is a little different from English.

Because after יכול/יכולה, Hebrew normally uses the infinitive.

• לתפור = to sew

So:

• יכולה לתפור = can sew / is able to sew

This is the standard pattern:

• יכול לקרוא = can read
• יכולה לכתוב = can write
• יכולה לתפור = can sew

את marks a definite direct object.

Since הבד means the fabric / the cloth, it is definite, so Hebrew uses את before it:

• לתפור בד = to sew fabric / cloth (indefinite, no את)
• לתפור את הבד = to sew the fabric / the cloth (definite, with את)

Important point: את usually is not translated into English. It is a grammar marker.

It can mean either the fabric or the cloth, depending on context.

The base noun is:

• בד = fabric / cloth

With ה:

• הבד = the fabric / the cloth

In many learning examples, both English translations are acceptable.

Yes. This is a very normal Hebrew word order:

subject + יכול/יכולה + infinitive + object

So:

• מכונת התפירה = subject
• יכולה = can / is able
• לתפור = to sew
• את הבד = the fabric

That makes the sentence sound natural and straightforward.

Yes, but the meaning changes.

• מכונת תפירה = a sewing machine
• מכונת התפירה = the sewing machine

So in your sentence, the form with ה makes the subject definite.

Because Hebrew grammatical gender is not the same as biological sex.

Every noun is assigned a grammatical gender, and other words agree with it.
מכונה is a feminine noun, so it takes feminine agreement:

• מכונה חדשה = a new machine
• המכונה יכולה = the machine can

This is just grammar.

It would agree with the new subject.

For example:

• המכשיר יכול לתפור את הבד. = The device can sew the fabric.
  (מכשיר is masculine singular, so יכול)

• המכונות יכולות לתפור את הבד. = The machines can sew the fabric.
  (feminine plural, so יכולות)

• המכשירים יכולים לתפור את הבד. = The devices can sew the fabric.
  (masculine plural, so יכולים)

So agreement is a key part of understanding the sentence.