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To solve the problem of determining which lines are parallel in the given diagram, observe the arrangement of each pair of lines:

1. The lines labeled \(m\) and \(n\) do not intersect and appear parallel.
2. The lines labeled \(k\) and \(l\) intersect, so they are not parallel.
3. The lines labeled \(x\) and \(y\) do not intersect and appear parallel.
4. The lines labeled \(i\) and \(j\) intersect, so they are not parallel.

Therefore, the correct pairs of parallel lines are:

• \(m \parallel n\)
• \(x \parallel y\)

From the options given below the diagram, the green button (x y) indicates the correct pairs of parallel lines.