Translation:Dat kan ik me niet veroorloven.
I think this construction might be one of the ones that causes me the most problems.
Intellectually I know how it works, but I've a habit of screwing up when an auxiliary verb is combined with a reflexive verb, as in this sentence.
I don't understand why "dat" is first. I wrote "Ik kan verroorloven dat niet."
Standard word order would be Ik kan me dat niet veroorloven. Like in English you can start a sentence with certain words to put more emphasis on them, compare I went to the beach yesterday (standard) and Yesterday I went to the beach (more emphasis on yesterday). So that's the reason the sentence starts with dat here. The (finite) verb comes in second position, and the subject comes directly after that. You need me because veroorloven is reflexive. And as it's another verb veroorloven comes at the end.
How would it be the sentence if it started with 'ik'?
When there is an auxiliary verb in dutch, the main verb assumes the very last position, the fourth position, so you can imagine that 'niet' is assuming the very last position of the non verb, non subject, non object word
A general word order to remember, in case there is an auxiliary verb: subject, auxiliary verb, object and main verb (always in the very last position). You should also check the positions of different adverbs, 'niet' is a negating adverb, a different class from time and place adverbs (there are other adverbs classes)
The pronouns are quite challenging. You are probably used to being able to interchange "mij and me", but "mij" is an object pronoun.
In this case the Dutch "reflexive pronoun" is needed because "Veroorloven" is a reflexive verb.
In the "Tips and Notes" https://www.duolingo.com/skill/dn/Reflexive-Verbs-and-Pronouns You can find the reflexive pronoun list.
When I started learning these lessons I kept the tips and notes page opened in a browser window, it can help be a quick reference until you have them memorized!