Question

Beginning with newly-formed igneous rock describe the processes and paths that could move the material through the rock cycle until it again forms newly cooled igneous rock

Answer 1

An Igneous rock can change from sedimentary to metamorphic and back again or vice versa. 
Metamorphic rocks form from heat and pressure 
Sedimentary rocks are formed when sediment is deposited out of air, ice, wind, gravity, or water flows carrying the particles in suspension.

Answer 2

The cooling and crystallization of magma forms new igneous rock. Weathering, erosion and deposition of the material could result in the transition to sedimentary rock. Heat and pressure could then result in metamorphic rock. If this rock melts and forms magma, it could again crystallize into igneous rock.