Your first step is to find the circumference of the earth, with the numbers given. You can do that by putting the radius of 6200 kilometres into the 2πr equation. That should get you a circumference of 12400π, or about 38,955.75 kilometres.
Next, you can use the rate the Jetson's car is going (180km/h) and divide the 38,955.75 by it to see how many hours it would take at that constant speed.
38,955.75 / 180 = 216.42 hours
Then you can divide that by 24 to get how many days