First, multiply each side of the equation by #color(red)(3)/color(blue)(8)#:

#color(red)(3)/color(blue)(8) xx 8/3 = color(red)(3)/color(blue)(8) xx 12/n#

#cancel(color(red)(3))/cancel(color(blue)(8)) xx color(blue)(cancel(color(black)(8)))/color(red)(cancel(color(black)(3))) = 36/(8n)#

#1 = 36/(8n)#

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

#color(red)(n) xx 1 = color(red)(n) xx 36/(8n)#

#n = cancel(color(red)(n)) xx 36/(8color(red)(cancel(color(black)(n))))#

#n = 36/8#

#n = (4 xx 9)/(4 xx 2)#

#n = (color(red)(cancel(color(black)(4))) xx 9)/(color(red)(cancel(color(black)(4))) xx 2)#

#n = 9/2#