First you’ll want to create a hex grid and have a polygon to match it to.
We’re going to clip the hexes to the exact edge of your state.
Start by going to Geoprocessing Tools > Clip…
We’ll then select the grid as the input layer and the state as the layer to clip to. Then Run in Background.
Look at that! Clipped right to the edge!
Note: Your grid is probably a temporary layer, so you’ll want to right-click it and save it as an actual shapefile!