Learn Dutch: Jouw ogen zien er een stuk beter uit wanneer je geen contactlenzen draagt. - Your eyes look much better when you do not wear contact lenses.

Een stuk literally means 'a piece', but when placed before a comparative adjective like beter (better), it acts as an intensifier meaning 'a lot' or 'much'. So een stuk beter means 'a lot better'. You could also use veel beter here, and the meaning would be exactly the same.

Why are the words zien, er, and uit spread out in the first half of the sentence?

These words all belong to the separable verb eruitzien, which means 'to look [a certain way]'. In a main clause, this verb splits: the core verb zien takes the second position, er follows closely behind, and the separable prefix uit is pushed to the end of the clause, right before wanneer.

Why does the verb draagt (wear) go at the very end of the sentence?

The word wanneer (when) introduces a subordinate clause. In Dutch subordinate clauses, all verbs are kicked to the very end. That is why the sentence ends with wanneer je geen contactlenzen draagt instead of keeping the verb right next to the subject je.

Why does this sentence use geen instead of niet for 'do not wear'?