lets find that out writing equations and solving them, a multiple of 1/6 is something like this (1/6)x, so we have
(1/6)x > 3/6
and
(1/6)y < 4/6
lets solve both equations:
(1/6)x > 3/6
x > 6(3/6)
x > 3
(1/6)y < 4/6
y < 6(4/6)
y < 4
So the number must be between 3 and 4, which is obvious, lets try with 3.5 then, that is 3 5/10 or 35/10 = 7/2 in fractional form, and lets try it out:
(1/6)(7/2) = 7/12
finally we compare with the original fractions:
1/6 < 7/12
2/12 < 7/12
So, it comply with being greater than 1/6, now lets compare with 4/6
7/12 < 4/6
7/12 < 8/12
therefore is also smaller than 4/6 and hence 7/12 is a multiple of 1/6 between 3/6 and 4/6