Learn Polish: Przecież brakuje panu czarnego tuszu. - You obviously lack black ink, sir.

The word przecież doesn't have one perfect English translation. It adds a tone of 'but obviously,' 'as you know,' or 'after all.' Here, it makes the statement sound like a reminder or a slightly surprised observation, like saying 'But sir, you are obviously out of black ink!'

Why do we say brakuje panu instead of using pan as the subject?

The verb brakować (to lack or be missing) uses an impersonal structure in Polish. The person who is missing something takes the dative case (panu), so literally this translates to something like 'there is a lack to you, sir.'

Why is the ink written as czarnego tuszu instead of the basic form czarny tusz?

The verb brakować always requires the thing that is missing to be in the genitive case. Since tusz is a masculine inanimate noun, its genitive form is tuszu, and the adjective czarny changes to its genitive form czarnego.

Could we change the word order to Przecież panu brakuje czarnego tuszu?

Yes, that is grammatically correct and means the same thing. However, putting the pronoun panu right after the verb brakuje is a very natural and common word order in Polish, as shorter pronouns generally sound best when tucked in after the verb.