der Mann, dessen Auto kaputt ist

One relative word is still missing, and it is the one that means whose. You will meet it constantly in writing; producing it is a smaller job than understanding it, so understanding comes first.

dessen — masculine and neuter. deren — feminine and plural. Both mean whose.

• Das ist der Mann, dessen Auto kaputt ist.

  That is the man whose car is broken.

  der Mann is masculine → dessen

• Das ist die Frau, deren Bruder in Berlin wohnt.

  That is the woman whose brother lives in Berlin.

  die Frau is feminine → deren

• Ich kenne die Leute, deren Wohnung wir gesehen haben.

  I know the people whose flat we saw.

  plural → deren

• Das ist das Kind, dessen Mutter Ärztin ist.

  That is the child whose mother is a doctor.

  das Kind is neuter → dessen

The habit from Lesson 3 still applies, and here only half of it does any work: the gender comes from the noun outside. der Mann → dessen. die Frau → deren. What follows inside the clause does not change that at all.

Look left of the comma to choose dessen or deren. Nothing to the right of it matters.

That is worth stressing because the noun that comes next is a trap. In der Mann, dessen Auto…, the word Auto is neuter — but the pronoun is dessen because der Mann is masculine. In die Frau, deren Bruder…, Bruder is masculine and the pronoun is still deren.

The second thing to notice is what disappears. German does not say dessen sein Auto — dessen already carries the possession, so the noun takes no article and no possessive. It sits there bare.

• der Mann, dessen Auto kaputt ist

  the man whose car is broken

  not "dessen das Auto", not "dessen sein Auto" — just dessen Auto

• die Kollegin, deren Mann in Köln arbeitet

  the colleague whose husband works in Cologne

And the verb goes to the end, as in every relative clause you have built: …, dessen Auto kaputt ist**.

One last comfort. These two forms are all there is at this level — there is no desseren, no plural of dessen. Two words, chosen by the noun on the left. When in doubt while reading, translate both as whose and carry on.