Gives 16 stamps to macy and 24 stamps to sebastian. naomi has 3 times as many stamps as macy and macy has twice as many as sebastian. how many stamps does naomi have at first

At first: 
Naomi --- x 
Macy y 
Sebastian -- 234 -x - y 

After the giving: 
Naomi --- x-16 - 24 
Macy --- y + 16 
Sebastian --- 234-x-t + 24 

x-16-24 = 3(y+16) ---> x - 3y = 88 
y+16 = 2(234-x-y+24) --> 2x + 3y = 500 

add them: 
3x = 588 
x = 196 
then in x-3y=88 
196-3y=88 
-3y=-108 
y = 36 

Naomi had 196 
Macy had 36 
Sebastian had 2