Final answer:
The type of immune response associated with Th1 cells and macrophages working to eliminate intracellular pathogens is cell-mediated immunity.
Step-by-step explanation:
The type of immune response regulated by Th1 cells secreting interferon-gamma (IFN-γ) when engaging macrophages displaying intracellular non-self-antigen on MHC Class II molecules is e) Cell-mediated immunity. This immune response involves frontline defenses such as macrophages that help to fight against intracellular pathogens like viruses or some bacteria. The Th1 cells, once activated, produce cytokines that enhance the macrophages' ability to digest and eliminate these intracellular threats. Furthermore, the Th1 response also works in synergy with cytotoxic T cells (Tc cells) in the destruction of these infected or even cancerous cells.