Naive Bayes considers each feature separately, i.e. features are independent given the class. The exact X is not in the training data, but each of its features has been seen before.
However, there is still a problem with P(own_house=true|No) which is zero according to training data (0 divided by 6). For this, we use Laplace smoothing to replace the zero with (0+1)/(6+4)=1/10. Now, Naive Bayes could assign X to a class.
Naive Bayes classifier compares
P(X, Class=Yes) = P(Class=Yes) * P(Age=middle|Yes) * P(has_job=false|Yes) * P(own_house=true|Yes) * P(credit_rating=good|Yes) = 9/15 * 3/9 * 4/9 * 6/9 * 4/9 =
P(X, Class=No) = P(Class=No) * P(Age=middle|No) * P(has_job=false|No) * P(own_house=true|No) * P(credit_rating=good|No) = 6/15 * 2/6 * 6/6 * 1/10 * 2/6 = 0.0044
and assigns X to Class = Yes.