Cutting some corners to keep this simple but:

Turbofans make more thrust than turbojets, because they employ a large fan driven by a jet engine. This way it can accelerate a large amount of air, and while the acceleration is less than what a turbojet engine does to the air that passes through it, the efficiency is greater anyway. Accelerating a large amount of air a little is better than accelerating a litte amount of air alot.

Turboshaft engines are basically jet engines that convert pretty much all of the energy of the exhaust jet into rotational movement, which is then routed through a gearbox to drive a propeller, rotor or whatever needs to be driven.

One could say the core engine is the same in all of the three cases here, what varies is how the energy of exhaust jet is used. Turbojet simply relies on the high speed of the exhaust as it is, turbofan uses most of the exhaust energy to drive the fan, and turboshaft uses all of the energy from the turboshaft to drive the output axle (and gearbox).

A turboshaft run by a turbofan makes little sense. It's like running a car with an outboard motor.

What you may be thinking about is a geared turbofan. They do exists, this engine employs a gearbox to reduce the rpm of the fan driven by the jet engine. This enables the use of larger fans, as the fan blade tip speed stays lower even though the blades are longer.

Cutting some corners to keep this simple but:

Turbofans make more thrust than turbojets, because they employ a large fan driven by a jet engine. This way it can accelerate a large amount of air, and while the acceleration is less than what a turbojet engine does to the air that passes through it, the efficiency is greater anyway. Accelerating a large amount of air a little is better than accelerating a litte amount of air alot.

Turboshaft engines are basically jet engines that convert pretty much all of the energy of the exhaust jet into rotational movement, which is then routed through a gearbox to drive a propeller, rotor or whatever needs to be driven.

One could say the core engine is the same in all of the three cases here, what varies is how the energy of exhaust jet is used. Turbojet simply relies on the high speed of the exhaust as it is, turbofan uses most of the exhaust energy to drive the fan, and turboshaft uses all of the energy from the exhaust to drive the output axle (and gearbox).

A turboshaft run by a turbofan makes little sense. It's like running a car with an outboard motor.

What you may be thinking about is a geared turbofan. They do exists, this engine employs a gearbox to reduce the rpm of the fan driven by the jet engine. This enables the use of larger fans, as the fan blade tip speed stays lower even though the blades are longer.