Hawaii lies in the Northern Hemisphere (latitudes 19°N–22°N) but the Eastern Hemisphere (longitudes 155°W–160°W).
The Western Hemisphere is defined as longitudes west of the Prime Meridian (0°) to 180°W. Hawaii's longitude (~155°W–160°W) places it east of the 180th meridian (antimeridian), which is the boundary between the Eastern and Western Hemispheres in the Pacific. Therefore, Hawaii is in the Eastern Hemisphere—along with most of Oceania, Asia, and Australia.
Because Hawaii is a U.S. state and culturally "Western," people assume it's in the Western Hemisphere. Geographically, it's not. The only U.S. state entirely in the Western Hemisphere is Alaska (specifically, the Aleutian Islands west of 180°).