First, eliminate the fractions and keep the equation balanced by multiplying each side of the equation by #color(red)(14)#.

#color(red)(14)(-3/2y - 9/7) = color(red)(14) xx -3/2#

#(color(red)(14) xx -3/2y) - (color(red)(14) xx 9/7) = cancel(color(red)(14))7 xx -3/color(red)(cancel(color(black)(2)))#

#(cancel(color(red)(14))7 xx -3/color(red)(cancel(color(black)(2)))y) - (cancel(color(red)(14))2 xx 9/color(red)(cancel(color(black)(7)))) = -21#

#-21y - 18 = -21#

Next, add #color(red)(18)# to each side of the equation to isolate the #y# term while keeping the equation balanced:

#-21y - 18 + color(red)(18) = -21 + color(red)(18)#

#-21y - 0 = -3#

#-21y = -3#

Now, divide each side of the equation by #color(red)(-21)# to solve for #y# while keeping the equation balanced:

#(-21y)/color(red)(-21) = -3/color(red)(-21)#

#(color(red)(cancel(color(black)(-21)))y)/cancel(color(red)(-21)) = 1/7#

#y = 1/7#