Answer: torment or tease (someone) with the sight or promise of something that is unobtainable.
Step-by-step explanation:
Dictionary Definition:
tan·ta·lize
/ˈtan(t)lˌīz/
verb
torment or tease (someone) with the sight or promise of something that is unobtainable.
"such ambitious questions have long tantalized the world's best thinkers"
excite the senses or desires of (someone).
"she still tantalized him"
Background:
The word comes from a greek (I think) myth about a king named Tantalus, who received eternal punishment in hell by being surrounded by luscious fruits, clear water, and food but being unable to move his body to reach it, and would forever feel hungry.