How could you plant an idea in someone's mind?

simply use a reversed psychology

Firstly one has to make sure that the person values your opinion and respects you and not just because of your seniority, but rather for your values. experience and knowledge. You must also value suggestions and or comments made by the person. This sets the platform for planting an idea. Then share the background why a solution has to be found. Make suggestions how problem can be solved, but be careful not to over sell your idea, what you want to achieve is for the person to buy into, is that it is their idea! When this is achieved you will achieve total buy in. Coaching, coaching is the answer!