From what I can see in the image, that appears to be USS George Washington (CVN-73) as there is a 73 on the side of the island.
USS George Washington (it would be much easier if it was just called USS Washington) went into drydock for mid-life refueling in 2017, so the image must be from before then.
JS Hyūga (DDH-181) was commissioned into service in 2009, so the image can be no older than 2009.
Wikipedia has another image of JS Hyūga and USS George Washington sailing in formation in 2013 after a joint exercise but the lighting and aircraft on deck are completely different.