Ответ:

  1. Peter is always looking at himself in the mirror!
  2. You two should prepare yourselves for the test.
  3. Have you ever taught yourself a new skill?
  4. The cat washes itself carefully every morning.
  5. We embarrassed ourselves by showing off.
  6. The girls entertained themselves with video games.

Reflexive pronouns agree with the subject: he → himself, you (plural) → yourselves, you (singular) → yourself, it → itself, we → ourselves, they → themselves.