What is the probability of rolling an even number on a die, under the condition that the number is less than 4

Question

So this problem is greatly confusing me. In the solution, using conditional probability, where A is the event of getting an even number:
$A=\{2,4,6\}$
And B is the event of getting a number smaller than 4:
$B=\{1,2,3\}$
Then $P(A|B)=P(AB)/P(B)=1/3$
Now, I don't understand why the answer is $1/3$. Isn't this question the same as "what is the probability of rolling an even number that is smaller than 4" for which there is only 1 favorable outcome out of 6 - number 2. So the solution would be $1/6$. What am I missing here? Is the solution miscalculated?