You must determine the properties of the two hot (black) wires. On your receptacle the bond between the two hot screws is broken. Unless you did that in removing the screws that means that probably one of the black wires is from a switch and the other black is hot all the time. Is the bond on the white side also broken? If that is the case, then you want to cap off the black to the switch and its paired white and use the other black and white to power the USB outlet.
Do not directly connect either black wire to a white or to ground. 'Cap-off' means to put a wire nut over the end so it cannot contact another wire or a ground. I assume your new device is a duplex receptacle with USB in the center right?
If one of the black wires is hot and the other is known to feed other receptacles or switches on the same circuit, you may join the two black wires and connect via a pigtail to the new receptacle (and of course do the same with the two white wires). But the missing bond on the black side means you should verify that one pair of wires (black and white) feeds. Make sure the second black is not hot.