Answer
$-\displaystyle \frac{4}{3}$
Work Step by Step
$y=mx+b$
is the slope intercept form: slope m and y-intercept b.
So, we solve $4x+3y=6$ for y:
$3y=-4x+6\qquad/\div 3$
$y=-\displaystyle \frac{4}{3}x+2$
$m=-\displaystyle \frac{4}{3}$