الخزانة نظيفة، وكمان المكتب ناشف بعد ما مسحته.

In Arabic, the verb to be is usually left out in the present tense.

So:

• الخزانة نظيفة = The cabinet is clean
• المكتب ناشف = The desk is dry

This is called a nominal sentence. Arabic does this very naturally in the present.

If you wanted the past, you would usually use كان:

• الخزانة كانت نظيفة = The cabinet was clean

Because the adjective has to match the noun in gender.

• الخزانة is feminine, so the adjective is نظيفة
• المكتب is masculine, so the adjective is ناشف

So the pattern is:

• masculine: نظيف, ناشف
• feminine: نظيفة, ناشفة

This kind of agreement is very important in Arabic.

Because here they are predicate adjectives, not adjectives directly attached inside a noun phrase.

Compare:

• الخزانة نظيفة = The cabinet is clean
• الخزانة النظيفة = the clean cabinet

In the first sentence, نظيفة is telling you something about الخزانة, so it does not take ال.

The same applies to:

• المكتب ناشف = The desk is dry
• المكتب الناشف = the dry desk

وكمان means and also, and too, or plus.

It breaks down as:

• و = and
• كمان = also / too / as well

So:

• الخزانة نظيفة، وكمان المكتب ناشف
  = The cabinet is clean, and the desk is also dry

كمان is very common in spoken Levantine Arabic. It is more conversational than a formal word like أيضًا.

It can mean desk or office, depending on context.

In this sentence, desk is the more natural meaning, because it says:

• المكتب ناشف بعد ما مسحته
  = The desk is dry after I wiped it

You usually wipe a desk so it becomes dry, which makes much more sense than office here.

They describe two different things:

• نظيفة = clean
• ناشف = dry

So something can be:

• clean but not dry
• dry but not clean
• both clean and dry

In this sentence:

• the cabinet is described as clean
• the desk is described as dry, specifically after being wiped

Here بعد ما means after.

So:

• بعد ما مسحته = after I wiped it

In this expression, ما is not negation. It is just part of the very common spoken pattern بعد ما.

So do not read it as after not....

A good way to remember it is:

• بعد ما + past verb = after doing something / after I did something

مسحته means I wiped it.

It breaks down like this:

• مسحت = I wiped
• ـه = it / him (masculine singular object)

So:

• مسحت + ه → مسحته
• meaning: I wiped it

In this sentence, it refers to المكتب, which is masculine.

Because ـه is a masculine singular object pronoun.

• المكتب is masculine
• الخزانة is feminine

So if the speaker meant the cabinet, Arabic would normally use ـها instead:

• مسحتها = I wiped it referring to a feminine noun

Since the sentence says مسحته, the object is understood to be المكتب.

It is clearly colloquial Levantine-style Arabic.

A few clues are:

• وكمان is a very common spoken word for and also
• ناشف is a very natural everyday colloquial word for dry
• the overall phrasing sounds conversational

A more formal / Standard Arabic version might look more like:

• الخزانة نظيفة، والمكتب أيضًا جاف بعد أن مسحته

That said, the original sentence is very natural for spoken Levantine.

A very literal reading would be:

• الخزانة = the cabinet
• نظيفة = clean
• وكمان = and also
• المكتب = the desk
• ناشف = dry
• بعد ما = after
• مسحته = I wiped it

So the literal structure is roughly:

The cabinet clean, and also the desk dry after I wiped it.

That sounds unnatural in English, but it helps show how Arabic is building the sentence.