An economic system where the means of production are privately owned.
In pure capitalism all means of production are privately owned. Under socialism no means of production is privately owned. In a mixed economy there is a mixture between the two. When we use a phrase like “under capitalism” or “in a capitalist economy” we are referring to pure capitalism. If we want to refer to a mixed economy it is important to specifically point that out and to detail in what manner it is mixed.
If you believe people should be able to own tools and use them to make new things, then you are in favor of (some degree of) capitalism.