This is the 966th most frequent Russian word.
такую
"Such" or "such a" (feminine accusative singular).
'Такую' here is part of the comparative structure 'такую же', emphasizing the identicality of the feminine noun (bag) as another instance.
Она купила такую же сумку, как у тебя.
She bought the same bag as yours.
'Такую' serves to emphasize the remarkable attribute (difficulty) of the feminine noun (road) chosen.
Почему ты выбрал такую сложную дорогу?
Why did you choose such a difficult road?
Here, 'такую' functions as a demonstrative adjective highlighting the degree of beauty in a feminine noun (painting).