Which layer of the earth is composed of iron and nickel, and has two main parts called the outer and the inner ?
a. the mantle
c. the crust
b. the core
d. the lithosphere

The Crust and Lithosphere (which are almost synonymous) are not typically divided into two distinctive layers, so we can reject them.

The correct answer is is the core: (b). The inner core is solid and it's made of iron and nickel. The outer layer is liquid and this is the reason for the differentiation of the two parts. 

The sun's parallax would be 180 degrees, greater than which you can't get.  so a. would be your anwser