Remember the below rules

for ax+by+c

x intercept = -c/a
y intercept = -c/b

slope = -a/b


if y intercept is positive i.e. 4
x intercept has to be positive for slope to be negative.

Therefore any non negative and non zero value for x intercept will result in negative slope.

Hence answer is 6.

one more hint:
-ve slope line will make angle > 90 with x axis
+ve slope line will make angle < 90 with x axis

another way to look at it is:

negative slope always run from left to right (in the X-Y plane) in downward direction.

So just draw XY Plane and a line intercepting at 4 going downward will run between Quad II and Quad I - so the x - intercept has to be positive.

in your case the only positive is 6 (ofcourse the line is making slope so it cant be 0 )

Slope = - Y int / X int
Y int = 4
Given slope is -ve

Hence X Int shud b +ve

1) X = -1 (Not possible) - Eliminate
2) X = 0 (Indefinite slope) - Eliminate
2) X = 6 - Possible....Select

Hope this helps

Thanks you all for the responses. It helped me to understand the problem.

Baskaran