the equation of the circle is x^2-8x+y^2+4y+11=0 find any coordinates that intersect the line y=-x-1

In your circle equation replace y with -x-1 and simplify, you should get the reduced quadratic

x^2 - 5x + 6 = 0
which factors and has solutions
x=2 or x=3

sub those x values into your y = -x-1 to get the y's and you are done!