In any probability distribution, all probabilities must add up to 1.
From the table, the random variable X can take values 0, 1, or 2 with probabilities:
P(X=0)=K
P(X=1)=3K
P(X=2)=5K
P(X=otherwise)=0
Since all probabilities must sum to 1:
K+3K+5K+0=1
9K=1
K=91
Therefore, K=91