Draw three circles with M inside to represent the men. Shade 2 of them to represent 2/3 of the men being married to a woman.
Just below that, draw 4 circles with W to represent the women. Shade 3 of the circles to represent 3/4 of the women married to a man.
Clearly the 2 shaded "M"s and 3 shaded "W"s don't match up in number, so we'll have to scale up the ratio as your teacher mentioned in the hint.
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We have the two fractions 2/3 and 3/4 to represent the men and women married.
Normally we try to get the denominators to be the same (for instance if we wanted to add the fractions).
However, in this case we want to have the numerators be the same.
The LCM of the numerators 2 and 3 is 6 because 2*3 = 6.
To get 2/3 to have a numerator of 6, we multiply top and bottom by 3, so (2/3)*(3/3) = 6/9
Similarly, we have 3/4 = (3/4)*(2/2) = 6/8
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The original fractions 2/3 and 3/4 are equivalent to 6/9 and 6/8 respectively.
We'll have a similar drawing after scaling up.
There are 9 circles for the men and 8 circles for the women. For each, 6 circles are shaded to represent married persons.
The ratio of men to women is 9:8 which is the final answer
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A numeric example:
The town has 90 men and 80 women.
2/3 of the men are married to women, so (2/3)*90 = 180/3 = 60 men are married to women.
3/4 of the women are married to men, so (3/4)*80 = 240/4 = 60 women are married to men
There are 60 married men/women couples.
Note the ratio of 90 men to 80 women can be written in the compact shorthand notation of 90:80.
Then divide both parts by the GCF 10 to get the final answer 9:8