First, multiply each side of the equation by #color(red)(24)# to eliminate the fractions. #color(red)(24)# is the lowest common denominator of the three fractions and eliminating the fractions will make the problem easier to work:

#color(red)(24)(5/8x - 1/3) = color(red)(24)(2x - 5/6)#

#(color(red)(24) xx 5/8x) - (color(red)(24) xx 1/3) = (color(red)(24) xx 2x) - (color(red)(24) xx 5/6)#

#(cancel(color(red)(24))3 xx 5/color(red)(cancel(color(black)(8)))x) - (cancel(color(red)(24))8 xx 1/color(red)(cancel(color(black)(3)))) = 48x - (cancel(color(red)(24))4 xx 5/color(red)(cancel(color(black)(6))))#

#15x - 8 = 48x - 20#

Next, subtract #color(red)(15x)# and add #color(blue)(20)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#15x - 8 - color(red)(15x) + color(blue)(20) = 48x - 20 - color(red)(15x) + color(blue)(20)#

#15x - color(red)(15x) - 8 + color(blue)(20) = 48x - color(red)(15x) - 20 + color(blue)(20)#

#0 + 12 = 33x - 0#

#12 = 33x#

Now, divide each side of the equation by #color(red)(33)# to solve for #x# while keeping the equation balanced:

#12/color(red)(33) = (33x)/color(red)(33)#

#(3 xx 4)/color(red)(3 xx 11) = (color(red)(cancel(color(black)(33)))x)/cancel(color(red)(33))#

#(color(red)(cancel(color(black)(3))) xx 4)/color(red)(cancel(3) xx 11) = x#

#4/11 = x#

#x = 4/11#