Mean =83+4+9+2k+10+8+6+(k+6)=8
⇒46+3k=64
⇒3k=18→k=6
If 4 is the mode then 4 must have the maximum frequency in the given series.
This means that either 2p or 2p+1 must be equal to 4.
Also, the question mentions that p is a natural number so 2p+1 can't be equal to 4.
∴2p=4→p=2
(k−2p)=6−4=2