Final answer:
The correct interpretation of R 4 is that Natalie has 4 apples left after filling 51 bags with 8 apples each, since 412 divided by 8 equals 51 with a remainder of 4.
Step-by-step explanation:
When Natalie divides 412 apples by 8 and gets an answer of 51 R 4, the interpretation of R 4 in this situation is that Natalie has 4 apples left after filling 51 bags. This is because when you divide 412 by 8, the quotient of 51 represents the number of full bags of 8 apples she can make, and the remainder (or the 'R' value) represents the number of apples that cannot be evenly distributed into another bag of 8. Hence, there are 4 apples remaining that cannot be packaged into a full bag.