Hello, EA!
I assume your difficulty is the setup.
Try setting up the facts in a table . . .
1.) Lita is fifteen yrs older than her sister Tess.
Six years ago, Lita was 6 times as old as Tess.
Find Their present ages.
Make a row for each person in the problem: Lita and Tess. Code:

    +         
Lita 
    +         
Tess 
    +         
Make a column for each time period in the problem:
. . Now and sometime in the Past. Code:
 Now  Past 
    +     +    +
Lita   
    +     +    +
Tess   
    +     +    +
"Lita is 15 years older than Tess."
. . Let $\displaystyle x$ = Tess' age (now).
. . Then $\displaystyle x+15$ = Lita's age (now).
Write those in the "Now" column. Code:
 Now  Past 
    +     +    +
Lita  x + 15  
    +     +    +
Tess  x  
    +     +    +
Six years ago, they were both six years younger.
. . Lita was $\displaystyle x + 9$ and Tess was $\displaystyle x  6$.
Write those in the "Past" column. Code:
 Now  Past 
    +     +    +
Lita  x + 15  x + 9 
    +     +    +
Tess  x  x  6 
    +     +    +
The equation always comes from the last column.
We are told: Six years ago, Lita was six times Tess.
. . . . . . . . . . . . . . . . . . . . $\displaystyle \downarrow\quad\;\;\downarrow\quad\;\downarrow \quad\;\,\downarrow\qquad\;\;\downarrow
$
and there is our equation: .$\displaystyle x + 9 \:= \:\;\;6\quad\times\quad(x  6)$
Now try it on the second problem . . .