If Q and S have at least two brands in common, then what is the maximum number of handsets that Q and S together can own?

Let's tabulate the conditions one by one.  

Since we have ten handsets, we have two cases

1: T owns 2 headsets
2: T owns 1 headset
Case 1 :
If T owns 2 handsets, then S owns 4 handsets
But Q owns handsets of three different brands.
So we are left with only 1 handset to be given between P and R.
This case will not serve the purpose
Case 2: T owns 1 handset.
If T owns 1 handset, then S owns 2 handsets
Since the person who owns Nokia does not own any other handsets 
It cannot be T as T and R have at least one headset brand in common
It cannot be Q as it owns three different brands. 
It cannot be S as it has 2 handsets and the person who owns Nokia doesn't own any other handsets.
So it has to be P : P owns a Nokia handset.

Since we have to maximise the number of handsets with Q and S together ,R and T owns 1 handset each i.e Samsung .

S owns 2 handsets of either Iphone or One plus ,Q owns 4 handsets

So maximum number of handsets that Q and S together can own is 7 

Hence C is the correct answer