Day after day , the earth made _ year-long journey around the sun
a. his
b. it's
c .its'
d. its

Day after day, the earth made its year-long journey around the sun.

His would be if you were referring to a male (animal, human, etc).
It's shows possession of something, the earth doesn't possess the year-long journey.
Its' is another way of showing possession if the thing that posses it already has an s on the end. (Example: Charles' car.)