to find the y intercept all you need to do is sub in x=0.
Hence p(0)= 6/-7 = - 6/7
to find the x intercept you need to find where p(x) = 0 however due to it being a fraction there is no value of x that would satisfies that situation as 6/(x^2+6x-7) = 0 is equlativent to saying 6=0 which is not true.
As for the slant asymptote. the answer is x/2 - 1/4 which for the explainable of this is very long. has it involes alot of work to find out
there are 2 asymptote you could use which are -1 and 1/2 and this is simply done by finding the values of x which gives an invaild answer. i.e. doesn't exist in the know mathematically world. (dividing by 0)
First you should declare that the divisor must be different than zero. Consequently you should first solve x^2 + 6x - 7 =/= 0
In order to find the x intercept solve p(x) = 0 and in order to find the y intercept solve p(0)
As for the asymptotes I'm not 100% how to approach it.