Nash, who is seated in the right foreground, is applying a dazzle camouflage scheme to a wooden ship model, which will then be tested for its effectiveness in a specially-designed observation theatre.
Given the historical prominence of all three of Nash's names, perhaps he was descended from venerable families in the South. One source states that Nash was born in Fleming County KY in 1882. There was a lawyer named Samuel Kercheval (1767-1845), who wrote an early well-known history of the Shenandoah Valley (A History of the Valley of Virginia). And Nashville TN was named for the Revolutionary War hero, Francis Nash (1742-1777), who also grew up in Virginia. Manley may also be a family name, and a quick look on the internet finds people who have name combinations like Kercheval Nash, Manley Nash, and so on.
So Manley K. Nash (1882-1947) remains a mystery more or less. One source (Edan Hughes, Artists in California 1786-1940) claims he studied art in Paris in 1905 (as did everyone at the time). When he returned to the US, he apparently lived briefly in (possibly) Harris TX, then moved to St Louis MO, where he painted scenery for the stage, and where other relatives may have settled. After World War I, he moved to southern California, and then, prior to 1930, to Oklahoma City OK. While on the West Coast, he must have made connections with Hollywood movie studios because he continued to paint stage sets for films and in 1938 (according to Hughes) "painted the burning of Atlanta for Gone With the Wind." Moving back to St. Louis, he may have taught at the School of Fine Arts at Washington University, where he himself had studied art as an undergraduate.
Not much to go on really. But we did find one other curious bit. It seems that in 1940, with Hollywood listed as his residence, Nash and another person named Arthur J. Thomas were granted a patent for a toothbrush (US Patent No 2246867) that features a "polishing and massaging element" that "combines with the bristles in cleaning and polishing the teeth [while] also imparting gentle massaging action to [the gums]." Their patent drawing is below.