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Let's calculate \(\frac{a}{b}\) for all the answer choices and check which ones are equal to \(\frac{6}{7}\)

A) \(\frac{36}{49}\) --> No

B) \(\frac{30}{35}\) = \(\frac{6}{7}\) --> Yes

C) \(\frac{14}{12}\) = \(\frac{7}{6}\) --> No

D) \(\frac{7}{8}\) --> No

E) \(\frac{3}{(7/2)}\) = 3 * \(\frac{2}{7}\) = \(\frac{6}{7}\) --> Yes

F) 0 --> No

All we need to do for this problem is find answer choices in which the both parts of the ratio are scaled up (or down) by the same factor.

This is true for Choice B, since \(6*5 = 30\) and \(7*5 = 35\).
It's also true for Choice E, since \(6*\frac{1}{2}=3\) and \(7*\frac{1}{2}=\frac{7}{2}\)

Answers: B and E
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My approach is:
1) The ratio of a to b is 6 to 7 means a/b = 6/7
2) After cross-multiplying, 7a=6b
3) Based on 7a=6b, let's use a common symbol to make calculation simplier, a=6β and b=7β
4) for this question we converted a and b into β (a=6β and b=7β)
5)Let's look to options.
Choice A) a=36,b=49 in other words 6β=36 and 7β=49 if we assume that β is 6 it is true for 36 BUT wrong for 49 so this option is wrong.
6) Use this method other options than you will see only B and E are true.