The problem consists of analyzing the visible line patterns through the cut-outs of two rotating discs to determine which line pattern belongs to the back disc. Let's carefully evaluate the given options and steps:
Observe the provided image showing four different positions of visibility through the front disc's cut-outs, considering the pattern revealed as the two discs rotate independently. The visible sections are fragments of the line pattern on the back disc.
Analyze each potential line pattern option:
For each option, try to match the segments seen through the cut-outs with those of the line pattern depicted on the option.
Focus on isolating key features from each visible section, such as line lengths, angles, or intersections. Check if they appear consistently across rotated views.
After comparing all options, option 3 (disc 3) provides a perfect match to the visible pattern when rotated:.
This pattern aligns precisely with the observable segments through both cut-outs across the illustrated positions.
Conclude the analysis confirming option 3 as the correct representation of the line pattern on the back disc.
By following these steps systematically, one can determine that disc 3 is indeed the correct choice.