IPA: //ˈkwoʊtəblɪ//
KK: /ˈkwotəblē/
In a manner that can be quoted or is worthy of being quoted.
The speaker expressed her ideas quotably, making them memorable for the audience.
Quotably → It is formed from "quote" (from Latin "quotare", meaning to mark a number or to cite) and "-ably" (meaning in a manner that can be). The word "quotably" means in a manner that can be quoted or suitable for quoting.
Think of 'quoting' someone — 'quote' means to cite, and '-ably' means in a way that can be done. So, quotably means something that can be cited.