I believe that every decision is either made logically or emotionally. From the brain, the heart, both, or neither of them.
For me, the best way I could think of this is with my characters that I create for my stories; that sometimes start looking like a book. They start from my brain, my mind, and the pieces of my heart find there way into them. Then I become attached to them and when I have to decide on away to get rid of them I shed a tear for every one of them. I know, it’s weird but, I never said I was normal.
For example, deciding an answer to a math problem or finding the best way to beat up the bad guy in video games. That’s all brain power; you use your brain to find the best way to do it.
Or deciding whether you are ever going to walk or just be reduced to being pushed around on a wheel chair. That was my uncle’s dilemma. The blood that was going to his legs became clotted in his knee joints to the point where it started to become painful for him to even stretch his legs. If he did not go into surgery then the doctors would have to amputate his legs. You would think that the choice would have been simple, but my uncle has been having money problems and did not have the best health insurance.
So, when it was time for him to choose, and amputation was the cheaper route. He was going to choose to loose his limbs. But, of course we, his family, helped him out with the money, the entire family (that was in the area) and he got the surgery. Now he can walk, like nothing ever happened.
Those were some examples of making decisions with your brain, heart, and both. The only example I can think of for maybe not using either of them would be instinct, to solve a problem. I have done my fair share of those, that I really care not go into.
When one or more of my characters has a problem, in any of my stories I think:
“What would I do if I were in their shoes?”
Then I make my decision either with my intellect, my feelings on the matter, or just go with the flow. Or use instinct and attack the problem full on and see what happens.