"Walk during your lunch hour."
Translation:Marche pendant ton heure de déjeuner.
"Promener" is transitive, i.e. you use it with an object (grammatical object, I mean) afterwards : "je promène mon chien" (typical example).
"to (have a) walk" is "se promener" (intransitive, or rather the "object" is the pronoun "se", as in "to walk one's self"). So in this exercise, it would be :
- Promenez-vous / Promène-toi pendant votre/ton heure de déjeuner.
This is imperative for pronominal verbs, which you haven't learned yet I suppose.
Yes, you can put "se promener" at the beginning of / in a sentence. And you could put an infinitive at the beginning of this sentence - but not that infinitive, and not with the original English sentence being "Walk during your lunch break".
You could have "se promener" starting as the subject of a sentence you pronounce : "Se promener est bon pour la santé" ("Walking is healthy", or rather "Having a walk is healthy"). Here we use "se" because it's about having a walk in general, i.e. me, you, anybody (impersonal : "se").
The infinitive is not necessarily at the start and/or subject of a sentence : "On conseille de se promener tous les jours" ("It's advised to have a walk every day" - again general, impersonal use)
In any case (start, end, subject, object...) you must agree that reflexive infinitive according to whom it applies to: "J'aime me promener" ("I like having a walk").
Thus, in this sentence, since we're talking about tu or vous ("your lunch hour"), you should phrase the infinitive like this : "Te (/Vous) promener pendant ton (/votre) heure de déjeuner".
But that is not a proper sentence; it's either an article title for instance, or the start of a longer sentence "Te promener pendant ton heure de déjeuner serait une bonne idée" (Having a walk during your lunch hour would be a good idea).
Finally, as you can read in the English translation just above, it starts with having : so, if you use a French infinitive as a subject like you would in this case, the English equivalent must have been a verb in -ing (i.e. "Walking during your lunch hour" in the exercise here) or to + verb ("To walk during your lunch hour").