with what / whereby
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with what
Question word that asks about the means, tool, or object with which an action is carried out. It corresponds to the phrasing 'mit was?' (with what?).
Womit hast du die Flasche geöffnet?
What did you open the bottle with?
'Womit' (with what/with which) is a pronominal adverb made up of 'wo-' and the preposition 'mit' (with). It asks about a thing or a means and literally means 'with what'.
Womit sollen wir anfangen?
What should we start with?
As a question word, 'womit' (with what) comes at the beginning of the sentence, followed by the finite verb. As a relative adverb, it introduces a subordinate clause in which the finite verb comes at the end.
Womit schreibst du den Brief?
What are you writing the letter with?
As a relative adverb, 'womit' (whereby/with which) can refer not only to a single noun, but to the content of the entire previous main clause. It then expresses a result or consequence.
Das Team hat das Projekt pünktlich abgeschlossen, womit alle zufrieden waren.
The team completed the project on time, which everyone was satisfied with.
In spoken language, the phrase 'Mit was?' (with what?) is often used for questions instead of 'womit' (with what). In written texts and more formal contexts, 'womit' is more common.
Mit was hast du das bezahlt?
What did you pay for that with?
so that / with it
'damit' and 'womit' both contain the idea of 'with something'. That is why they can easily be confused. You use 'damit' when you state a purpose or when you refer to something already known: with this thing. You use 'womit' in questions or in relative clauses when you ask about, or refer to, the means or object. A simple guide is: 'damit' often gives an answer or states a goal, while 'womit' asks about the means or introduces a clause with a reference.
Womit hast du die Tür geöffnet?
What did you open the door with?
Ich schreibe mir den Termin auf, damit ich ihn nicht vergesse.
I write down the appointment so that I don't forget it.