Cut butter and shortening into chunks and cream them together. Gradually add sugar. Add eggs one at a time.
Stir together flour and nutmeg. Alternate flour and eggnog: one cup flour, 1/2 cup eggnog, one cup flour, the rest of the eggnog, and then the rest of the flour. Keep the mixer going slowly, scraping down the edges as necessary.
Stir in the coconut, and then the vanilla, rum, and coconut flavoring.
Pour into prepared pan(s) and place on the cookie sheet in the preheated oven. Bake for 90 minutes.
Allow to cool 10 minutes in the pan, then turn out onto a wire rack to finish cooling.
Sprinkle with powdered sugar and serve. Also good with a scoop of ice cream on the side.