。
I was lucky to find a good babysitter.
Literal
Good babysitter [subject-が] could-be-found lucky was.
ベビーシッター is the katakana loanword. 見つけられる is the potential of 見つける ('to find'). て-form + 幸運だった ('was lucky') — the te-form links reason (finding) to consequence (luck). A natural expression of gratitude.