To answer the question, it is enough to evaluate the distance from the point (0,0) to the line  y = -x - 4.


There is a remarkable formula which ideally suits for this need.


    Let the straight line in a coordinate plane is defined in terms of its linear equation 

         a*x + b*y + c = 0,

    where "a", "b" and "c" are real numbers, and let P = (,) be the point in the coordinate plane. 

    Then the distance from the point P to the straight line is equal to

        d = .


Regarding this formula, see the lesson
    The distance from a point to a straight line in a coordinate plane
in this site.


Your equation in general form is  x + y + 4 = 0.


So, your coefficients are a= 1, b= 1, c= 4,   = 0,  = 0.


Substitute this data    into the formula to get the distance under the question


     =  = .


Answer.  The distance under the question is .