One dozen has 12 units.
So 6 and a half dozen shall have 6.5 ×12 = 78 cookies.
She sold
[tex] 3\frac{2}{6} =3\frac{1}{3} =\frac{10}{3} [/tex] dozens
So cookies she sold
= [tex] =\frac{10}{3} (12)
= \frac{120}{3}
=40 [/tex]
Number of cookies left = 78 - 40 = 38
So 38 cookies
[tex] =\frac{38}{12}
=\frac{19}{6}
=3\frac{1}{6} [/tex]
Tara is left with [tex] 3\frac{1}{6} [/tex] dozens