ANSWER
First of all I turn the fractions back to their improper form that is to say;
6 3/4 - 4 11/12
= 27/4 - 59/12
after that I get the LCM of 12 and 4 which is 12
= (²⁷/⁴ × 12) - (⁵⁹/¹²× 12) /12
= (81 - 59) /12
= 22\12
since the answer is requested for in the simplest form the the difference in form of a mixed fration is 1 10/12 which is reduced to 1 5/6 therefore the answer is 'B'