Groak is an uncommon and obscure word that means to stare longingly at someone else's food or drink. It's not a word that's used very often, but there are several synonyms that convey the same meaning. One such word is "gawk," which means to stare openly and stupidly at something or someone. Other synonyms for groak include "ogle," which means to look at someone or something with desire or interest, and "peek," which means to take a quick and furtive glance at something. Ultimately, there are many different ways to express the act of staring at someone else's food or drink, even if the word "groak" isn't one that's commonly used.