Final answer:
Rocks are likely to undergo ductile deformation under high temperature and high pressure because these conditions allow them to bend and flow.
Step-by-step explanation:
The rock's tendency to undergo ductile or brittle deformation is influenced by temperature and pressure conditions. High temperature and high pressure typically cause rocks to deform in a ductile manner because these conditions allow the rock to bend or flow rather than fracture. Conversely, at low temperatures and pressures, rocks are more prone to brittle deformation, fracturing instead of bending. Therefore, the combination of factors that would cause a rock to undergo ductile deformation as opposed to brittle deformation is high temperature and high pressure.