For any probability distribution, all probabilities must add up to 1.
From the table:
P(X=2)=k5
P(X=3)=k7
P(X=4)=k9
P(X=5)=k11
All probabilities sum to 1:
k5+k7+k9+k11=1
Since all fractions have the same denominator:
k5+7+9+11=1
k32=1
k32=1
32=k
Therefore k=32
4k=432
4k=8
Therefore, the value of 4k is 8.