16 points. find x and y intercepts and show work.

i’m looking for number six.

What an awful question. 
y = (x^4 - 3x^3 + 4x)^2
y = x^2(x^3 - 3x^2 + 4)^2 
Go to Wolframalpha and put the above equation into the input line.
You see that there are 2 solutions at -1
There are 2 solutions at 0
There are  2 solutions at 2
You know that there are 2 solutions for each because the graph just touches the x axis. I wouldn't both to try and solve this thing using algebra.

that's what the graph would leave you to believe. There are 2 other solutions and they must be imaginary.  

Note to moderator. Wolfram dot com just shows graphs. the work is mine and I'm just using a tool to explain my answer.