Learn Dutch: Wij proberen de datum af te spreken.

Afspreken (to agree on / to arrange) is a separable verb. It is made of the prefix af and the base verb spreken. When a separable verb is used in a te clause, the word te is sandwiched exactly between the prefix and the verb, creating a three-word phrase: af te spreken.

Would it be wrong to say te afspreken?

Yes, that would be incorrect. For normal verbs, te goes right before the whole verb. But with separable verbs, English speakers often accidentally put te at the front. Remember to split the separable verb and put te in the middle!

Why does de datum (the date) come before the verb phrase instead of after it?

In Dutch, verbs in a te clause are always pushed to the very end of the sentence or clause. Because of this word order rule, the object you are trying to agree on (de datum) has to come before the action (af te spreken).

Could I use om ... te in this sentence instead of just te?

Yes, you absolutely can! With the verb proberen (to try), you can optionally add om at the beginning of the clause. It means the exact same thing and is very common: Wij proberen om de datum af te spreken.