It takes the appealing fruit company about 16 hours to pull, box, and ship 500 cartons of apples. how many cartons can they box and ship in 2 days?

We are given the ratio
16 hours: 500 cartons

Let's divide both sides by 16
For the left side we have 16/16 = 1
For the right side we have 500/16 = 31.25

The ratio is now 
1 hour: 31.25 cartons

Next multiply both sides by 48 (since 48 hours = 2 days)
1 hour: 31.25 cartons
48*1 hour: 48*31.25 cartons
48 hours: 1500 cartons

So they can box and ship 1500 cartons in two days

1500