6. As shown in the right figure, a rectangular block with length, width, and height of $15 \mathrm{~cm}, 5 \mathrm{~cm}, 4 \mathrm{~cm}$ respectively, has a part cut out with length, width, and height of $y \mathrm{~cm}, 5 \mathrm{~cm}, x \mathrm{~cm}$ respectively ($x, y$ are integers). The remaining part has a volume of $120 \mathrm{~cm}^{3}$. What is $x+y=$.
【Answer】 15
【Analysis】 $15 \times 5 \times 4-y \times 5 \times x=120$ solves to $x y=36 ; 36=1 \times 36=2 \times 18=3 \times 12=4 \times 9=6 \times 6$, for $x, y$ being integers, and $x<4, y<15$, so $x=3, y=12 . x+y=15$