This is the 3535th most frequent Japanese word.
落とし
"落とし" (otoshi) means "drop" or "fallen item."
Here, '落とし' is the verb '落とす' in past tense, used literally to indicate dropping something uncontrollably.
彼は財布を落としました。
He dropped his wallet.
In this case, '落とし' as the conjugated verb '落とす' describes intentionally placing something (medicine) into a liquid.
彼女は水に薬を落とした。
She dropped medicine into the water.
Here, '落とし所' represents a figurative usage of '落とし' to indicate compromise or conclusion in a discussion or issue.