To evaluate a question in this manner it is important to have in mind that the rule of PEMDAS would apply. This rule basically gives you the order in which the mathematical signs will be taken when the question does not arrange the expressions into parenthesis. Hence, the correct order is division before addition and subtraction (Parenthesis, Exponent, Multiplication, Division, Addition and Subtraction).
The expression can now be re-arranged thus;
3/8 - [1/4 ÷ 6/7]
3/8 - [1/4 * 7/6]
3/8 - [7/24]
3/8 - 7/24
The LCM is 24 and that now gives you
9/24 - 7/24
2/24
1/12