The line k has a positive slope m and it passes through the point (-4,

I am not sure if my way of approach is correct. But still I ended up with the answer..

Area of the triangle formed by the line k with X & Y axis is 54.
1/2 * Base * Height = 54

Here Base refers to the x-intercept in units and Height refers to the y-intercept in units
So --> X (or Base) * Y (or Height) = 108

We know that the line k passes through the point (-4,6) and has a positive slope.
Therefore, the point where the line meets the X-axis must be definitely greater than -4 i.e greater than 4 units from the origin(Base)
Similarly, the point where the line meets the Y-axis must be definitely greater than 6 i.e greater than 6 units from the origin(height)

There are a handful of factors that multiply into 108 but only one satisfies the above condition.
9 and 12 -- valid since it satisfies both of the above criteria

the below ones do not
27 and 4
18 and 6
36 and 3
108 and 1

So the y intercept can be either (0,12) or (0,9)
and x-intercept can be either (-9,0) or (-12,0)

We slope m = (y2-y1)/(x2-x1) --> 12/9 or 9/12 i.e 4/3 or 3/4

Answer is 3/4 (B)