How to find equivalent resistence of this mixed circuit?
There are many techniques that you could use to find the currents and voltages in the circuit, including the node-voltage method and the mesh-current method. In general, these methods will all rely on Kirchhoff's laws and Ohm's law.

Since you have only a resistor network and a single source you can combine resistors until you have a single resistor and the source...then find the current being provided by the source. That must be the same current as is flowing through R4, so now you know the voltage across R4. Work backwards through your simplifications of the resistor network, finding more detailed current and voltage information as you work your way back to the original circuit.