Ответ:

  1. of — Ben's trying to think of a name for his new pet. (придумать)
  2. by — She phoned her mother by mistake. (по ошибке)
  3. about — Don't worry about the test. (волноваться о)
  4. of — It was a waste of money. (трата денег)
  5. at — The sailors were lost at sea. (в море)
  6. to — She hasn't written to me recently. (писать кому-либо)