How does government intervention in market distort market equilibrium?
Whenever the government intervenes in a market it disrupts market equilibrium in some way. The exact way that it does this differs depending on how the government intervenes.
The government can cause shortages of some commodity by setting a price ceiling for that commodity. If it does this, there is more demand than supply at the price the government orders.
Alternately, the government can cause surpluses by setting price floors. An example of this is minimum wage, which causes more people to want to work compared to how many people employers want to hire.
Government actions can stimulate or reduce supply (by taxes or regulations or subsidies) or demand of a product (by changing the amount of money available) as well.
There are many different ways that government actions can distort market equilibriums. But in all cases, the government's actions do end up either raising or lowering the price and quantity of goods and services.