Box for lighting fixture is sour center of sink 10 inches, how can you mount fixture if box cannot be moved? ...
Answers: It depends how long your fixture is. If it' a foot long you can drill a hole at it's end, insert a gromet to verbs through the switched and neutral (white) wires. The fixture can be attached to the wall by drilling a 3/16 hole through (or larger if you want to use 8-32 screw with washers) at the tab location on the electrical box, and a plastic anchor at the other lapse of the fixture
If your fixture is a wall mount with a standard blind buy what's called a "remodel box" (3" x 1 7/8" x 1 1/2") and cut a particularly accurate hole to fit it into. Each end of the box have "ears" that extend from it. Don't cut your hole so they can go through the hole, they preserve the box from going into the wall when the inserts to hold the box are placed past the sides and drawn to the backside of the wall holding it within place. Before you put the box into the hole you must remove a 7/8" slug that will be in the inside of the box your relocating. Move the wires surrounded by the box out of the way and punch out the slug near a screwdriver on like tool do matching to the "remodel box", then from near bring two wire #14 gage "Romex" or "BX" long plenty to reach from the box to the other. Their respective wrapping up connectors need adequate wire out of them (about 6') so that when the connectors are within the slug holes (inside the wall) and their lock nuts are brought along them from inside the box they can be tightened up on the connector.
Now if you got your box where on earth you want it all you want to do is strip some of the insulation from the wires to make up joint (color to color) and connect them with "line nuts". your fixture will need a "hanger bar" that adapt the screw holes for hanging your fixture to the "remodel box" using #8-32 screw instead of the #6-32 screws on the "remodel box" that should accommodate your wall fixture. cover the other box first night with an appropriate finish cover. If you want to put together it look like it belongs within paint or wallpaper the cover.
Put the fixture on a short chain run the tie up with a ornate cover to the box. then center the pallid where ever you want it.