Kevin has 4 choices of appetizers, 4 choices of meats, 6 choices of vegetables, 4 choices of desserts, and 7 choices of drinks. To find the total number of different meals he can order, we need to multiply the number of choices for each category:
4 appetizer choices × 4 meat choices × 6 vegetable choices × 4 dessert choices × 7 drink choices = 2,688
Therefore, Kevin can order 2,688 different meals. So the answer is option C.