The government can influence private producers of goods and services in a variety of ways. It can regulate businesses. It can tax certain activities. Finally, it can subsidize activities to encourage them. Any of these can influence private producers of goods and services.
Government can directly regulate businesses. We can see many examples of this in our economy. The government tells businesses what the minimum wage that they can pay is. It tells businesses what they must do to keep their employees safe. It tells them that they have to make products with certain safety features (such as requiring that cars have seat belts and air bags).
Governments can tax activities to reduce the extent to which those activities will be undertaken. A carbon tax, for example, would raise the price of using fossil fuels. This would tend to move people away from using such fuels. Conversely, a government can subsidize various activities. For example, the government of the United States subsidizes various farming activities. This encourages the raising of those crops.
In these ways, governments can influence what private producers make and how they make them.