Learn Dutch: Wij werken allebei op de afdeling. - We both work in the department.

Allebei is the most common and natural way to say "both" in everyday Dutch. While you could technically say wij werken beiden, the word beiden sounds much more formal and written. Note that allebei never gets an extra -n at the end, regardless of whether it refers to people or things.

Why does allebei come after the verb instead of before it?

In Dutch, distributive words like allebei (both) and allemaal (all) usually act like adverbs. When they refer back to the subject (in this case, wij), they are placed right after the conjugated verb. So, Dutch literally says "We work both in the department."

Why do we use the preposition op instead of in for "in the department"?

Prepositions rarely translate perfectly word-for-word. In Dutch, you work op een kantoor (in an office) and op een afdeling (in a department). It is simply a fixed prepositional combination that you have to memorize.

Could I emphasize "both" by starting the sentence with Allebei werken wij...?

No, you generally cannot start this sentence with allebei. Because allebei refers back to the subject, that subject (wij) needs to be introduced first so it is clear who you are talking about.