Final answer:
The best word to fill in the blank is 'receptive,' as it conveys the idea of being open to considering requests, which is the intended meaning in the sentence.
Step-by-step explanation:
The sentence "I was confident that after Dad had eaten a good meal, he would be more _____ to my request for the use of the car." is best completed using the word receptive. While all the options given—amenable, receptive, responsive, agreeable—have similar meanings in the context of being open or yielding to suggestions, 'receptive' is the most appropriate word here as it particularly implies a willingness or readiness to accept or consider something, such as a request. Hence, after eating a good meal, it is likely assumed that dad would be in a better mood and hence more open to considering requests.