The new leader lost most of his followers because he was so blank that he was unwilling to listen to and consider the ideas of those around him.

a. palpable
b. obdurate
c. traumatic
d. supine

The new leader lost most of his followers because he was so obdurate that he was unwilling to listen to and consider the ideas of those around him.

Explanation:

The word obdurate is the only word of the listed that makes sense in the given context. It means stubbornly refusing to change one's opinion or course of action; determined to act in a certain way despite what everyone else says or does. Its synonym is stubborn, but obdurate is a more formal option. So, we could say:  

The new leader lost most of his followers because he was so stubborn that he was unwilling to listen to and consider the ideas of those around him.

The meanings of other words do not fit.

Palpable means so intense that it's almost tangible, or able to be felt or touched.

Traumatic means deeply disturbing or distressing, or relating to physical injury (in medicine).

Supine means lying flat on one's back, or failing to act as a result of moral weakness.