1In 2-quart heavy saucepan, heat 8 oz of the white chocolate, the whipping cream and rum over low heat, stirring constantly, until chocolate is softened and mixture can be stirred smooth. Remove from heat; transfer to small bowl. Place plastic wrap over surface of mixture. Refrigerate about 2 hours until mixture is firm enough to hold its shape.
2Line cookie sheet with waxed paper. Scoop rounded teaspoonfuls of white chocolate mixture onto cookie sheet; roll lightly to shape into 1-inch balls. Freeze 15 minutes. Heat oven to 350°F. Bake coconut in a shallow pan for 5 to 7 minutes, stirring occasionally, until golden brown.
3In small microwavable bowl, microwave remaining 4 oz white chocolate uncovered on High 45 to 60 seconds, stirring once, until softened and chocolate can be stirred smooth. Place coconut in resealable food-storage plastic bag or between sheets of waxed paper; crush slightly with rolling pin. In shallow dish, place coconut. Dip each truffle in melted white chocolate; coat immediately with coconut. Return to cookie sheet; refrigerate 10 minutes or until firm. Store covered in refrigerator.