First, convert the mixed number into an improper fraction:
#(color(red)(1 7/8) - 3/4) * 2/3 => #
#(color(red)(1 + 7/8) - 3/4) * 2/3 =>#
#(color(red)((8/8 xx 1) + 7/8) - 3/4) * 2/3 =>#
#(color(red)(8/8 + 7/8) - 3/4) * 2/3 =>#
#(color(red)(15/8) - 3/4) * 2/3#
Next, we can subtract the two fractions within the parenthesis. However, before doing this we need to put the fractions over a common denominator:
#(color(red)(15/8) - color(blue)((2/2 xx 3/4))) * 2/3 =>#
#(color(red)(15/8) - color(blue)(6/8)) * 2/3 =>#
#(color(red)(15) - color(blue)(6))/8 * 2/3 =>#
#9/8 * 2/3#
Now, we can factor and cancel common terms before multiplying the fractions:
#9/8 * 2/3 =>#
#(3 * 3)/(2 * 4) * 2/3 =>#
#(color(red)(cancel(color(black)(3))) * 3)/(color(blue)(cancel(color(blue)(2))) * 4) * color(blue)(cancel(color(blue)(2)))/color(red)(cancel(color(black)(3))) =>#
#3/4#