Explanation

In △ABD the triangle inequality gives 10 − 6 < x < 10 + 6, i.e. 4 < x < 16. In △BCD it gives 18 − 6 < x < 18 + 6, i.e. 12 < x < 24. Together 12 < x < 16, and the keyed option is (b) 12, the lower bound of the admissible range.