How much is a ms66 1908 saint gualdens 20 dollar nomoto gold coin worth?

To set things straight and so that you can find your coin when doing searches, that's ST GAUDENS and NO MOTTO.

Numismedia lists a retail fair market value of an MS66 no-motto St. Gaudens double eagle at roughly $3800 for a Philadelphia coin, and 10 times that for a Denver coin.

In any case you need to be sure that your coin has been certified by one of the major grading services. MS66 is a stratospheric level for a coin and only a trained expert can assign that grade reliably.