In a traditional economic system you might see people rely on farming and using resources that they can make themselves. A disadvantage of this is that they take longer to make things. An advantage is that everyone is very close and work well together. This economic system can be found in places like Latin America.
In a command economy a big part of it is controlled by a centralized power. A disadvantage of this system is that all of the decisions are made by the government and the people have no say. An advantage of this system is that everyone will always have a job and won't be unemployed. This economic system is an example of a prison
In market economy the people control everything that happens. There is little to no government power involved. A disadvantage of this is that many monopolies can be formed. An advantage is that the product is very accessible to the consumer. You can find this type of economy in stores.
A mixed economy is a combination of command and market, there is some government interference but most of the decisions are privately made. A disadvantage of this is that it can be unequal. An advantage of it is that the government can interfere when a business is doing something wrong and help fix it. An example is a school.