The diameter of the Earth is stated in the question as 7928 miles. Inch , Foot , Yard and Mile are units for measuring length in the U.S. customary system.
The conversion factor for converting mile to kilometer , stated by you is 1.609.
So to convert mile into kilometer , it needs to be multiplied by the conversion factor.
1 mile = 1.609 km
Therefore 7928 miles = 7928*1.609 km
= 12756.152 km
Now we have to convert Kilometers into Centimeters.
We know that 1 km = 1000 meter
and 1 meter = 100 centimeter
Therefore , 1 km = 1000*100 centimeters
= 100000 centimeters
Now this is to be used as conversion factor for converting kilometers into centimeters.
Therefore , 12756.152 km = 12756.152*100000 centimeters
= 1275615200 centimeters
So, 7928 miles = 1275615200 centimeters
= `1.2756152*10^9 cm`