Line Plots · Superchallenge problem

Lena has lots of sticks that are $\dfrac{1}{4}$, $\dfrac{1}{2}$ and $\dfrac{3}{4}$ inch long. She chooses exactly $6$ sticks whose lengths add up to exactly $3$ inches, and makes a line plot of them. How many different line plots could she make? (Two line plots are different if some mark has a different number of X's.)