With how much money did she start?

A woman spent two-thirds of her money. She lost two-thirds of the remainder and then had $4 left. With how much money did she start?

Let M be the money the woman had with her initially.

The money she spent = $\dfrac{2}{3}$ * M
Remaining = M -  $\dfrac{2}{3}$ * M =  $\dfrac{1}{3}$ * M
The money she lost =  $\dfrac{2}{3}$ * ( $\dfrac{1}{3}$ * M ) = $\dfrac{2}{9}$ * M
Remaining = $\dfrac{1}{3}$ * M - $\dfrac{2}{9}$ * M= $\dfrac{1}{9}$ * M

=> $\dfrac{1}{9}$ * M = 4
=> M = 9 * 4 = 36

She had $36 at the start.