الفاتورة على هذه الورقة، لكنها تحتاج إلى توقيع أمي.

In Arabic, the present-tense to be is usually not written or spoken in simple sentences like this.

So:

الفاتورة على هذه الورقة
literally looks like
the invoice on this paper

but it means
The invoice is on this paper.

This is a very common Arabic pattern called a nominal sentence.

Because فاتورة ends in ـة (the tāʾ marbūṭa), which usually marks a feminine noun.

So even though an invoice is not biologically female, it is grammatically feminine in Arabic. That is why later in the sentence Arabic uses feminine agreement:

• لكنها = but it / literally but she/it
• تحتاج = it needs in the feminine singular form

Because ورقة is a feminine singular noun, so it takes the feminine singular demonstrative هذه.

• هذا = this (masculine)
• هذه = this (feminine)

So:

• هذا الكتاب = this book
• هذه الورقة = this paper

In Arabic, when a noun comes after a demonstrative like هذا or هذه, it is normally definite, so it usually has الـ.

So the standard pattern is:

• هذا الكتاب = this book
• هذه الورقة = this paper

For English speakers, this can feel a little unusual, because English does not say this the paper, but Arabic does use both the demonstrative and the definite article together.

على usually means on, upon, or sometimes over, depending on context.

Here it gives location:

• على هذه الورقة = on this paper

So the first clause is describing where the invoice is located.

لكنها is made of:

• لكن = but
• ها = her / it

So لكنها means but it here.

The pronoun ها refers back to الفاتورة, which is feminine singular. In fully vocalized Arabic, you may see لكنّها.

Because its subject is الفاتورة, which is feminine singular.

The verb احتاج / يحتاج means to need.
Here the form تحتاج agrees with a feminine singular subject:

• الفاتورة تحتاج = the invoice needs

In English we use it, which does not show gender for most objects, but Arabic still requires grammatical gender agreement.

In Modern Standard Arabic, احتاج إلى is the normal pattern for to need.

So Arabic says:

• تحتاج إلى توقيع
  literally: it needs to a signature

but naturally this means:

• it needs a signature

This is just how the verb is used in standard Arabic. English speakers often want to drop the preposition, but in MSA إلى is the usual choice with يحتاج.

توقيع means signature or signing, depending on context.

In this sentence, it clearly means signature:

• توقيع أمي = my mother’s signature

It is a verbal noun, but you can often think of it simply as the regular noun signature.

This is an iḍāfa construction, often called a genitive/possessive construction.

Structure:

• توقيع = signature
• أمي = my mother

Together:

• توقيع أمي = my mother’s signature

A few useful things to notice:

1. The first noun in an iḍāfa usually does not take الـ.
2. The second noun tells you whose thing it is.
3. Arabic does not use an apostrophe like English does.

So instead of signature of my mother or my mother’s signature with apostrophe, Arabic simply puts the two nouns together.

The ي is the attached possessive pronoun meaning my.

So:

• أم = mother
• أمي = my mother

This same suffix appears with many nouns:

• أبي = my father
• كتابي = my book
• اسمي = my name

So in توقيع أمي, the phrase literally contains mother-my, which English expresses as my mother.

Yes. فاتورة can mean bill or invoice, depending on context.

For example:

• in a restaurant, it may mean the bill
• in business or paperwork, it may mean the invoice

So the exact English word depends on the situation, even though the Arabic word is the same.

A fully vocalized version would be:

الفاتورةُ على هذه الورقةِ، لكنها تحتاجُ إلى توقيعِ أمي.

A learner does not need to memorize every ending right away, but the main points are:

• الفاتورةُ is nominative because it is the topic/subject of the first clause
• الورقةِ is genitive because it comes after على
• تحتاجُ is in the indicative
• توقيعِ is genitive because it comes after إلى
• أمي is the second part of the iḍāfa

If you are still early in your studies, it is enough to recognize the structure even if you are not producing all the case endings yet.