First, we multiple each side of the equation by t(t + 2)# to eliminate the fractions and keep the equation balanced:

#tcolor(red)(cancel(color(black)((t + 2)))) xx 6/color(red)(cancel(color(black)((t + 2)))) = color(red)(cancel(color(black)(t)))(t + 2) xx 4/color(red)(cancel(color(black)(t)))#

#t xx 6 = (t + 2) xx 4#

#6t = 4t + 8#

Next, substract #color(red)(4t)# from each side of the equation to isolate the #t# term while keeping the equation balanced:

#6t - color(red)(4t) = 4t + 8 - color(red)(4t)#

#(6 - 4)t = 4t - color(red)(4t) + 8#

#2t = 0 + 8#

#2t = 8#

Now, divide each side of the equation by #color(red)(2)# to solve for #t#:

#(2t)/color(red)(2) = 8/color(red)(2)#

#(color(red)(cancel(color(black)(2)))t)/cancel(color(red)(2)) = 4#

#t = 4#