Radio Astronomy Systems Research Group

There are multiple answers. Presented here is only one possible solution.

Start both hourglasses. When the 4 minute one runs out, there will be 3 minutes left on the other. Flip the 4 to restart it. When the 7 minute glass runs out, there will be 1 minute left on the 4 minute hourglass. (At this point, 7 minutes have passed.) Flip the 7 minute glass over. When the 4 minute glass empties, there will be 1 minute of sand in the 7 minute glass. (Now 8 minutes have passed.) Flip the 7 over once more for the final minute.