Problem-solving is a great form of communication only when someone asks you for advice. Supportive skills are more rare and tend to be much more difficult for a person to learn. Supportive communication is the opposite of problem-solving. You aren't supposed to give advice or say what you think if asked. Even when asked, you need to determine what the person asking for advice is thinking about doing before you rush in to give advice.
Supportive communication means allowing the other person to feel good about solving a problem.
If you think about most communication, you discover they involve demonstrating our own intelligence and abilities. It means allowing others to talk about their situation without interruptions or arguments. Support means the other person knows you are there with them and will listen and not attack them. Supportive communication is very powerful and requires effort to do well. You can't be both needy and supportive for very long.