يمكن أن تتصفح فهرس المكتبة بشرط أن يكون متاحا.

يمكن literally means it is possible. In Modern Standard Arabic, يمكن أن + present verb is a very common formal way to express can or may.

So:

• يمكن أن تتصفح = you can browse
• more literally: it is possible for you to browse

This wording is a bit more formal and impersonal than some everyday alternatives.

After يمكن, Arabic normally uses أن before another verb.

So the pattern is:

• يمكن أن + present tense verb

Here:

• يمكن أن تتصفح

Grammatically, أن also puts the following present-tense verb into the subjunctive. In fully vocalized Arabic, that would be:

• تتصفحُ → تتصفحَ

In normal Arabic writing, short vowels are usually not written, so both forms appear simply as تتصفح.

تتصفح is the present-tense form of the verb تصفّح, which means to browse, to leaf through, or to look through.

In this sentence, it means you browse or you are browsing in structure, but because it follows يمكن أن, the overall meaning becomes you can browse.

A few useful points:

• base verb: تصفّح
• present form here: تتصفح
• intended subject: you (masculine singular in standard grammar)

If the sentence were addressed to a woman, the form would usually be different, such as تتصفحي after أن.

Arabic often does not use an explicit subject pronoun when the verb already shows who the subject is.

So instead of saying:

• أنت تتصفح

Arabic can simply say:

• تتصفح

because the verb already carries the subject information.

In this sentence, the subject you is understood from تتصفح. Adding أنت would usually only be done for emphasis or contrast.

Word by word:

• فهرس = catalog, index
• المكتبة = the library

Together, فهرس المكتبة means:

• the library catalog
• literally: catalog of the library

This is a very common Arabic noun structure called iḍāfa.

Because this is an iḍāfa construction, often translated as the X of the Y or the Y's X.

In an iḍāfa:

• the first noun normally does not take ال
• the second noun can make the whole phrase definite

So:

• فهرس المكتبة = the library catalog

Even though فهرس has no ال, the whole phrase is definite because المكتبة is definite.

That is why الفهرس المكتبة would be wrong in standard Arabic.

بشرط means on condition, provided that, or subject to the condition that.

It is made of:

• بـ = a preposition, often meaning with, by, or in expressions like this on
• شرط = condition

So بشرط is a fixed expression meaning:

• provided that
• on the condition that

In this sentence:

• بشرط أن يكون متاحا = provided that it is available

Because Arabic usually prefers a full clause after بشرط when expressing a condition.

So the normal pattern is:

• بشرط أن يكون ...

Here:

• أن introduces the clause
• يكون means be
• متاحا means available

So the phrase literally works like:

• on condition that it be available

Using يكون makes the condition complete and grammatically clear in formal Arabic.

The hidden subject of يكون refers back to فهرس المكتبة.

So the meaning is:

• provided that it is available
• where it = the library catalog

Because فهرس is:

• singular
• masculine

the verb is also singular masculine:

• يكون

And the adjective is masculine singular too:

• متاحا

Even though المكتبة is feminine, the head noun of the phrase is فهرس, so agreement follows فهرس, not المكتبة.

In fully vocalized Arabic, this word would be written:

• متاحًا

The final ا is part of the normal spelling of many indefinite accusative nouns and adjectives with tanwīn fatḥ.

Here متاحًا is accusative because it is the predicate of يكون in a كان-type structure.

So:

• hidden subject of يكون = nominative
• متاحًا = predicate, accusative

In ordinary Arabic text, the vowel marks are usually omitted, so you often see:

• متاحا

instead of the fully marked:

• متاحًا

Yes, this sentence sounds fairly formal and natural in Modern Standard Arabic.

Some alternative ways to express a similar idea are:

• يمكنك تصفح فهرس المكتبة بشرط أن يكون متاحًا
• تستطيع تصفح فهرس المكتبة إذا كان متاحًا

These alternatives differ slightly in tone:

• يمكن أن تتصفح = formal, impersonal
• يمكنك تصفح = also formal, very common
• تستطيع = more direct, often closer to you are able to

The original sentence is completely normal for formal written Arabic.

A careful MSA pronunciation would be:

yumkinu an tataṣaffaḥa fihrisa al-maktabati bi-sharṭi an yakūna mutāḥan

A word-by-word guide:

• يمكن = yumkinu
• أن = an
• تتصفح = tataṣaffaḥa
• فهرس = fihrisa
• المكتبة = al-maktabati
• بشرط = bi-sharṭi
• أن = an
• يكون = yakūna
• متاحا = mutāḥan

In everyday reading, many speakers do not pronounce all the final case endings fully, but this gives you the formal grammatical pronunciation.