Refer to figures.
In a variable pitch propeller, the engine is governed to run at a set RPM throughout the flight range. The propeller governs the engine at this set rpm by the use of a device known as a constant speed unit (CSU) and by means of a flyweight governor. Any variations in engine power output (throttle pulled back or forward), which would otherwise produce a change in RPM, are sensed by the CSU which alters the propeller pitch angle to keep the rpm constant. If the throttle is pulled back, the propeller pitch would automatically decrease (fine pitch) but the RPM will remain the same, and vice-versa.

Free turbine engine here refers to free-turbine turboshaft which is a form of turboshaft or turboprop gas turbine engine where the power is extracted from the exhaust stream of a gas turbine by an independent turbine, downstream of the gas turbine. The power turbine is not mechanically connected to the turbines that drive the compressors, hence the term "free", referring to the independence of the power output shaft (or spool). This is opposed to the power being extracted from the turbine/compressor shaft via a gearbox.

Note: We placed this question in this sub-section since it is primarily about propeller properties. How the power is generated is not as relevant.