I think I've interpreted the problem correctly . . .
Not sure what you mean by "about two-thirds of the way from top to bottom".
There is a right-angled triangle, base is 10cm plus 6cm, side is 12 cm, hypotenuese is unknown.
There is a line about two-thirds (at the 10 and 6) of the way from top to bottom which is x.
She needs to work out x.
The answer is 7.5cm but we don't know how to get that answer.
But here's my diagram.
Using Pythagorus: .
12 | | * x
| | *
| | *
* - - - - - * - - - - - - - *
From the similar right triangles: .