First, multiply both sides of the equation by #color(red)(24)# to eliminate the fractions while keeping the equation balanced:

#color(red)(24)(5/12g + 2/3) = color(red)(24) xx 1/8#

#(color(red)(24) xx 5/12g) + (color(red)(24) xx 2/3) = cancel(color(red)(24))3 xx 1/color(red)(cancel(color(black)(8)))#

#(cancel(color(red)(24))2 xx 5/color(red)(cancel(color(black)(12)))g) + (cancel(color(red)(24))8 xx 2/color(red)(cancel(color(black)(3)))) = 3#

#10g + 16 = 3#

Next, subtract #color(red)(16)# from each side of the equation to isolate the #g# term while keeping the equation balanced:

#10g + 16 - color(red)(16) = 3 - color(red)(16)#

#10g + 0 = -13#

#10g = -13#

Now, divide each side of the equation by #color(red)(10)# to solve for #g# while keeping the equation balanced:

#(10g)/color(red)(10) = -13/color(red)(10)#

#(color(red)(cancel(color(black)(10)))g)/cancel(color(red)(10)) = -13/10#

#g = -13/10#