Question

which process allows energy produced in a stars core to reach its surface?
conduction through solid layers
evaporation of outer gases
radiation and convection through the stars interior
magnetic field transfer

Explanation:

Stars are not solid (so conduction through solid layers is wrong). Evaporation of outer gases doesn't transfer energy from the core. Magnetic field transfer isn't the main way for core - energy to reach the surface. In stars, energy from the core reaches the surface via radiation (photons moving through regions) and convection (hotter, less - dense gas rising and cooler, denser gas sinking).

Answer:

Radiation and convection through the star's interior