What are the three parts that make up earth's mantle?
a.) mesosphere, asthenosphere, ionosphere
b.) thermosphere, mesosphere, asthenosphere
c.) mesosphere, asthenosphere, bathysphere
d.) ionosphere, thermosphere, bathysphere
e.) mesosphere, asthenosphere, outer layer

E.) Mesosphere, Asthenosphere, Outer layer
Unfortunately there is no standard terminology for three mantle layers. 
I can be sure that "ionosphere" and "thermosphere" refer 
only to atmospheric layers, so you can rule out A, B, and D. 
"Mesosphere" may be used to refer to an atmospheric layer, 
but is also often used to refer to a mantle layer. 


, 
so I'll go with E even though I don't like it much. 
I guess what is meant by "outer layer" is the part of the lithosphere 
that does not match crustal composition.