Learn Dutch: Jullie hebben veel verplichtingen af te handelen. - You have many obligations to deal with.

This structure expresses that you have active tasks waiting to be done, which maps perfectly to the English "have [something] to do". Here, hebben is your main verb, the tasks you possess (veel verplichtingen) act as the object, and the action you need to perform goes at the end with te + infinitive (af te handelen).

Why is "te" placed right in the middle of "afhandelen"?

afhandelen (to deal with / to process) is a separable verb, made up of the prefix af and the core verb handelen. When you use te with a separable verb, it is always sandwiched directly between the prefix and the verb. Notice that it is written as three separate words: af te handelen.

Could I just use "moeten" instead of "hebben te" here?

Yes, you could say Jullie moeten veel verplichtingen afhandelen (You must deal with many obligations). However, hebben ... te changes the nuance. It emphasizes that you physically or metaphorically possess a list of tasks that are sitting there waiting for you, rather than just stating a general obligation.

What nuance does the prefix "af" add to "handelen" in this context?

The base verb handelen generally means "to act" or "to trade". Adding the prefix af often gives a sense of completion, checking off a list, or finishing. Therefore, afhandelen means to completely deal with, process, or finalize a task so that it is officially off your plate.