You can’t solve a problem that is unidentified or something that you identify in different ways. So, start by asking, “How do you identify the problem at hand?” Then, each of you shares what you think the problem is. Clarify and fill in details as necessary. End with each of you summarizing the problem and then agreeing on what exactly it is you are trying to resolve. Only then should you try to come up with possible solutions.
Each of you should come up with at least three possible ways to address the problem, put them in order of preference and then share with each other. This keeps you both from digging in on your own idea; you both see that there are several possible solutions.
Then rate each other’s solutions on a scale of 1 to 10 to find which ones are most agreeable to both of you. The benefit here is that more than a simple yes/no to the idea, you are sharing how much you like the ideas.
If no solutions are agreeable to both, then try to negotiate or compromise. “What would it take to make this possible solution worth a try?” “What might be a short-term solution and we can revisit in a while?” This type of conversation moves you toward solutions rather than looking at the obstacles.