1 1/5 a

------ = -----
-6 3/7 4 1/6

I read that as:

1 1/5 / -6 3/7 = a / 4 1/6

(6/5) / (-45/7) = a / (25/6)
(6/5)(-7/45) = 6a/25
-14/75 = 6a/25
450a = -350
a = -350/450 = -7/9