Channel Filter: Show Items with Two Specific Tags

Filter for Content Items that have “Main Shot” or “Product Shot” assigned in the tagbox “Media type”.

{
	"kind": "OrFilter",
	"filters": [
		{
			"kind": "TermFilter",
			"field": "basicInformation.mediaType._refId",
			"term": "648b76b163654189be7b6638b31fb243"
		},
		{
			"kind": "TermFilter",
			"field": "basicInformation.mediaType._refId",
			"term": "d019419aae9a4eaeb715d35efa0e61d7"
		}
	]
}

For tagboxes filter on the unique ID - not on the name. You find the ID in the URL when you open the list item.
For single tagboxes (tagboxes with only one value) you don’t need a nested filter.