How can we determine the economic profit in the following scenario? The question was: What is Pat’s shutdown point and what is Pat’s economic profit if it shuts down temporarily? The answer was: The shutdown point is the price that equals minimum average variable cost. To calculate total variable cost, subtract total fixed cost ($10—when output is zero, total variable cost is $0, so total cost at zero output equals total fixed cost) from total cost. Average variable cost equals total variable cost divided by the quantity produced. The average variable cost of producing 2 pizzas is $10 a pizza. Average variable cost is a minimum when marginal cost equals average variable cost. The marginal cost of producing 2 pizzas is $10. So Pat’s shutdown point is a price of $10 a pizza. When Pat shuts down the economic “profit” is actually an economic loss equal to Pat’s fixed cost. In particular Pat’s economic loss is $10." What calculation was used to find the economic profit?

If I understand your question correctly, you are trying to determine what Pat’s economic profit will be when he produces 2 pizzas.  If this is what you are asking, it is impossible to find the answer using only the information that you have given.  In order to find out what Pat’s economic profit is, we would need to know how much money Pat received for selling the two pizzas.
As you can see in the link below, economic profit equals total revenue minus total cost (this has to include both explicit and implicit costs).  Let us assume that the table you have attached shows Pat’s total costs.  The problem is that we still need to know how much revenue he received.
You have stated that Pat’s economic profit is actually -$10.  That means that his revenue had to be $10 lower than his costs.  The table shows that the cost of producing the two pizzas was $30.  Therefore, his revenue had to be $20, meaning that each pizza sold for $10.   This has to be the amount of revenue he got because 20 minus 30 = -10.
So, the equation that you are supposed to use to find economic profit is total revenue minus total cost.  Therefore, you need to know both total revenue and total cost to find economic profit.  Presumably, the revenue that Pat received is shown elsewhere in your assignment.
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