You need to have your denominators the same in order to perform addition or subtraction with fractions. The LCD of these two terms is 12. To change the terms you must first understand the fact that any number can be multiplied by one, and it will not change the original number. (as 5 x 1 = 5). The reason this is so important is because when dealing with fractions you can multiply it by one, or the equivalent, to change terms.
In order to make 2/3 have a denominator of 12, we need to multiply it by 4. Since we can multiply any number by 1, and 4/4=1, we can multiply 2/3 by 4/4 and get 8/12. (note we do not need to worry about the whole number term as it will not change, i.e. 12 * 4/4 = 48/4 = 12). Doing the same for the other term, we need to multiply 3/4 by 3/3 and get 9/12. Now you simply do the math.
12 8/12 - 6 9/12 = 6 (-1)/12
Since you have a negative numerator, you must borrow from the whole number:
6 = 12/12 => 5 12/12 - 1/12 = 5 11/12
There you go.
In order to make 2/3 have a denominator of 12, we need to multiply it by 4. Since we can multiply any number by 1, and 4/4=1, we can multiply 2/3 by 4/4 and get 8/12. (note we do not need to worry about the whole number term as it will not change, i.e. 12 * 4/4 = 48/4 = 12). Doing the same for the other term, we need to multiply 3/4 by 3/3 and get 9/12. Now you simply do the math.
12 8/12 - 6 9/12 = 6 (-1)/12
Since you have a negative numerator, you must borrow from the whole number:
6 = 12/12 => 5 12/12 - 1/12 = 5 11/12
There you go.
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71/12 or 5 11/12