The equilibrium price for a product in the market is the point where for a particular price the quantity that the producer is willing to supply at that price is equal to the quantity that the consumer is willing to pay at that price.
The supply and demand can be represented as curves on a graph where the y-axis displays the price and the x-axis displays the quantity. In the question the supply equation is Qs = 10p - 100 and there are two different categories of customers with a demand equation given by Qda = 90 - 4p and Qdb = 70 - 16p.
The equilibrium price for the customers in the category a can be calculated by equating Qs and Qda, this gives
10p - 100 = 90 - 4p
=> 10p + 4p = 90 + 100
=> 14p = 190
=> p = 190/14
Similarly for the category b, equating Qs and Qdb gives
10p - 100 = 70 - 16p
=> 100 + 70 = 10p + 16p
=> 170 = 16p
=> p = 170/16
The equilibrium price for the customer in category a is 190/14 and that for customers in category b is 170/16