First, subtract #color(red)(6/(v + 3))# from each side of the equation to consolidate the fractions:

#4/(v + 3) - color(red)(6/(v + 3)) = -color(red)(6/(v + 3)) + 6/(v + 3) + 2#

#(4 - 6)/(v + 3) = 0 + 2#

#-2/(v + 3) = 2#

Next, multiply each side of the equation by #color(red)(1/2)# to simplify the equation while keeping the equation balanced:

#color(red)(1/2) * -2/(v + 3) = color(red)(1/2) * 2#

#cancel(color(red)(1/2)) * -color(red)(cancel(color(black)(2)))/(v + 3) = 2/2#

#-1/(v + 3) = 1#

Then, multiply each side of the equation by #color(red)(v + 3)# to eliminate the fraction while keeping the equation balanced:

#color(red)(v + 3) * -1/(v + 3) = color(red)(v + 3) * 1#

#cancel(color(red)(v + 3)) * -1/color(red)(cancel(color(black)(v + 3))) = v + 3#

#-1 = v + 3#

Subtract #color(red)(3)# from each side of the equation to solve for #v# while keeping the equation balanced:

#-1 - color(red)(3) = v + 3 - color(red)(3)#

#-4 = v + 0#

#-4 = v#

#v = -4#