The equation -x^2+2x+6=2x-3 represents the intersections between a parabola and a line, the equation of the parabola is on the left side of the equation f(x)= -x^2+2x+6 and the equation of the line os on the right side g(x)=2x-3.
The general form of the equation of a parabola is f(x)=ax^2+bx+c, when a is greater than zero (positive) the parabola opens upwards, when it is negative the parabola opens downwards, in this case, a= -1, then the parabola that represents this equation should open downwards, then the answer is either the first or the second graph.
The equation of a line is given by the general form g(x)=mx+b, where m is the slope of the line, when m has a positive value the value of the y-coordinate of the line increases as x increases, between the first and the second option the only graph that has a positive slope line is the second one.
Then, the correct answer is the second option.