There are a lot of ratios here to keep track of. First, jot them down in abbreviated format:
d:f = 7:2
m:f = 2:3
b:d = 4:3
m:b = ?
To find the ratio of m to b, start combining the given ratios. To combine d:f and m:f, create a common term for f. Multiply the first ratio by 3 and the second by 2:
d:f = 7:2 = 21:6
m:f = 2:3 = 4:6
d:f:m = 21:6:4
Now incorporate b. Multiply the third ratio by 7:
b:d = 4:3 = 28:21
d:f:m:b = 21:6:4:28
Now extract the m:b ratio:
m:b = 4:28 = 1:7, choice (E).