Final answer:
The coach uses the technique of honestly sharing observations to establish trust and rapport with the client by validating the client's feelings and inviting self-reflection.
Step-by-step explanation:
In the conversation between the coach and the client, the coach is using the technique of B. honestly sharing observations. This technique is evident when the coach reflects the client's feelings back to him, indicating a clear and accurate understanding of the client's struggle. By doing so, the coach not only validates the client's feelings, making him feel heard and understood, but also gently challenges him to consider whether the motivation to quit smoking is his own or if it's more about his partner's desires. This approach can help establish trust and rapport by showing empathy and allowing the client to feel supported while also being encouraged to reflect on his personal motivations.