The two given functions are "linear". Their graphs are straight lines and lines are determined by two points. For example, for p= 10- 2x, if x= 0 the p= 10- 2(0)= 10 and if x= 5, p= 10- 2(5)= 0 so (0, 10) and (5, 0) are two points on the graph. Mark those points on your graph and draw the straight line through both points. Do the same for the second equation, p= 5x/2+ 2.
As for finding the "market equilibrium point" algebraically, that must be the point where the two lines cross so that (x, p) there must satisfy both equations. That means that p= 10- 2x= 5x/2+ 2. Solve the equation 10- 2x= 5x/2+ 2 for x and use that to find the corresponding p.
"The one that he taught us is way different from he wants us to answer" makes no sense because you haven't said what "the way he taught us" is.