【Adhere】 means to stick fast, to be devoted, or to carry out a plan. Using that glue, the wallpaper should 【adhere】 to the wall quickly. They have adhered to that particular faith for many years.
We are taking your advice and adhering to the revised plan.
【Cohere】 means to hold together as part of the same thing.
Generally, the film’s subplots failed to 【cohere】 .