The correct answer is Stubborn. The word 'obdurate' describes someone who is stubbornly refusing to change their opinion or course of action, an unyielding and obstinate person. Therefore, the synonym for 'obdurate' would be a word that conveys a similar sense of inflexibility and resistance to persuasion. 'Stubborn' perfectly captures this meaning, referring to someone who is determined not to change their mind or attitude.
Option A, Flexible, is incorrect because it is an antonym of obdurate. Flexible means capable of bending easily without breaking, or able to be easily modified to respond to altered circumstances, which is the opposite of being unyielding.
Option B, Yielding, is incorrect because it is also an antonym of obdurate. Yielding means giving way to pressure or persuasion, or compliant, which is contrary to the meaning of obdurate.
Option D, Merciful, is incorrect. Merciful means showing compassion or forgiveness, especially to those over whom one has power. This word is unrelated in meaning to obdurate, which describes a characteristic of temperament concerning stubbornness, not compassion.