A probability distribution table is given with some known values and some unknown values in terms of k.
In any probability distribution, all probabilities must add up to 1.
Adding all the probabilities and setting them equal to 1:
P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)=1
0.1+k+0.2+2k+0.3+k=1
0.6+4k=1
4k=0.4
k=0.1
P(X<3) means the probability that X is less than 3.
This includes X=0,1,2 (not 3).
P(X<3)=P(X=0)+P(X=1)+P(X=2)
P(X<3)=0.1+k+0.2
P(X<3)=0.1+0.1+0.2
P(X<3)=0.4
Therefore, P(X<3)=0.4