This problem is not a word problem but should be solved through the Line Wizards through Algebrator.  The equation for a line with slope of -6 through a point (-4,6) calculates to be y=-6x-18.  The x-intercept can be solved for by setting y=0 and solving for 'x' (x=-3).  These calculations are shown in the appended images. 

To help you clearly understand our desktop software and how appropriate it may be for your needs, please use one of the following links to obtain a free trial of the program:

Windows: http://www.softmath.com/tr/alg51win-tr-en.exe

Mac: http://www.softmath.com/tr/alg51mac-tr-en.dmg