It is very very simple and single step answer question.It is based on the Thevenine theorem and Maximum power transfer theorem.
when switch is open , voltage across two terminals is given as 2V this is nothing but this is the thevenine voltage.(Vth)
It is determined for any circuit just by opening the any branch in the circuit.
Next given is maximum power is transferred to Rp. Maximum power will transfer to Rp only if the resistance seen across the Rp is the thevenine resistance. The Thevenine Resistance between the termianals can be determined as follows.
first open any branch where you want to find the Thevenine Resistance. and next set all independent sources to Zero that is short the voltage source and open circuit the current sources.
then we will have only resistos and determine the total resistance seen from the terminals.
in the above circuit. try  total resistance will be (R1 parallel with R3) + (R2 parallel with R4) this is R th(thevenine resistance)
now form thevenine ciruit.by placing Vth in series with Rth and Rp(which we removed earlier)
and now current Ipmax is given. there is single loop apply kvl and determine the unknowns?
if you are not able to take this out send me an email at vinodh2308(it is gmail)
i will make a video on this and  will post in youtube.