Double Latch Stone prevent the blocks from moving by locking them in place, just like Latch Stones.

To remove them, you need to match the locked blocks with identical blocks or use items like Arrow Bombs/Double Bombs to blow them up but you need to blow them up twice in order to get rid of them entirely.

If you blow or match them with identical blocks, it turns into a regular Latch Stone so you need to blow/match them again to get rid of it entirely.