There are $4$ separate large boxes, and inside each large box there are $3$ separate small boxes, and inside each of these small boxes there are $2$ separate smaller boxes. How many boxes, counting all sizes, are there altogether?
To count the total number of boxes, I need to consider how many boxes are inside each other. I can start from the outermost layer and work my way inwards. There are $4$ large boxes, so that's the first term in my sum. Inside each large box, there are $3$ small boxes, so I need to multiply $3$ by the number of large boxes, which is $4$. That's the second term in my sum. Inside each small box, there are $2$ smaller boxes, so I need to multiply $2$ by the number of small boxes, which is $3 \times 4 = 12$. That's the third term in my sum. There are no more boxes inside the smaller boxes, so I can stop here. To get the total number of boxes, I need to add up the three terms I found: $4 + 3 \times 4 + 2 \times 12$. Using the order of operations, I can simplify this expression by doing the multiplications first and then the additions: $4 + 12 + 24$. Finally, I can add these numbers to get the final answer: $40$. 