This dotted net folds into a die. Three faces meet at the corner marked by the orange dot. How many dots are there on those three faces altogether?

Fold the row 1, 3, 6, 4 into a ring with the 2 as the lid. The ring closes with 4 coming round next to 1, so the left edge of the 2 lies along the top of the 4, and the top-left corner of the 2 sits where 4 and 6 meet. The corner holds 2, 4 and 6: $2+4+6=12$. (6 adds 2, 1 and 3, the squares nearest the dot in the flat net, but 2 and 1 meet at a different corner.)