Step 1Heat the oven to 350 degrees. Lightly butter and flour a 13-by-9-inch baking pan. Set aside.
Step 2Sift together the flour, baking soda, cinnamon and salt in a bowl. Set aside.
Step 3Beat the eggs and sugar until light, about 3 to 4 minutes. Beat in the oil, buttermilk and vanilla. Stir in the flour mixture just until blended. Gently stir in the pineapple, carrots, nuts and coconut.
Step 4Bake until a toothpick inserted in the center of the cake comes out clean, 55 to 60 minutes.
Step 1Combine the sugar, buttermilk, butter, corn syrup and baking soda in a saucepan. Bring to boil. Boil 5 minutes. Remove from the heat and stir in the vanilla.
Step 2Pierce the hot cake all over with a fork. Pour the frosting over the top. Let stand until cool.