C3 Functions confused about

You've got the right idea with the sketch; but note that it starts at x=0 and looks like y=2x until you hit x=2. (So are you sure it goes negative?)

Try drawing a sketch on graph paper and label the graph a bit more; where does it go through zero? What is its maximum value before it goes back down again?

Then to answer the three parts it will be helpful to accurately draw y=2, and y=4-x/4. You should be able to see the pattern emerging as the line y=2 crosses your graph (a) to find a general solution, and by drawing y=4-x/4 you'll be able to see how many solutions there are (b).

Finally, for (c), you need to find the exact x-values where y=4-x/4 crosses the periodic function. The first part of the periodic function looks like the line y=2x, but stops at x=2. What line does the part that then starts from x=2 look like? (Hint: Its gradient is 2, but what is its y-intercept?) By finding the exact equation of the function within each interval where it crosses y=4-x/4 you will be able to solve for x explicitly.

Hope I helped!