The circumference of the Earth is calculated through the equation,

C = 2πr

where C is the circumference and r is the radius.

Substituting the given to the equation,

C = 2π(6.38 x 10³)

C = 12760π km

We determine the number of hours that needs to be spent in order to walk around the calculated circumference. This can be calculated through the equation.

t = distance / speed

Substituting the known values,

t = (12760π km) / (4 km/h)

t = 3190π hours

Then, we calculate for the number of days given that only 12 hours is spent per day for the walk.

number of days = (3190π hours) / (12 hours/day)

number of days = 835.14 days

*ANSWER: 635.14 days*