In Monster Harvest, you cannot actually drop any items from your inventory. To potentially pick back up later, or get rid of it because you need the space for more important items. But you can trash the item, which is more or less the same thing, but it means the item is gone for good. You cannot reclaim it later.
To trash an item in Monster Harvest, you need to select the item you want to delete permanently, and this will move the item from your inventory and display it above the trash can. When displayed there, you need to highlight the trash can, which will turn blue with a dark green border around it, to indicate that it has been selected, and then press A.
If playing on PC, it's a lot easier to do this because you can click and drag or click and click—no need to cycle through everything like on a controller.
Remember, this will eliminate the item for good, so do not use it for anything valuable. Only use it for useless things in your inventory like rocks or wood and the like. The trash can will only be really needed at the start of the game, as you have minimal inventory space.
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