。
Calm down and tell me from the beginning.
Literal
Calmly from-the-beginning talk-try-[imperative].
~てごらん is a soft, friendly imperative — 'try doing X, why don't you.' Gentler than plain imperative 話せ; warmer than 話してください. Often used by parents, teachers, or doctors encouraging someone to open up. Comes from ご覧になる (honorific 'look'), the original sense being 'try it and see.'