Step 1: Treat the transformation as a single geometric operation.
Instead of checking letter by letter, treat the whole two-line label as one picture. The example shows this picture after a $180^{\circ}$ turn in its own plane, the same as picking up the label and spinning it half way around like a clock hand.
Step 2: Note the two effects a half turn always produces.
A half turn does two things at once: it puts the bottom line where the top line was, and it turns every character so it only reads correctly if you also turn your head upside down. A genuine rotation never produces just one of these effects alone.
Step 3: Use this as a filter on the four choices.
Check P, Q, R and S against both effects together. Any option that keeps the original line order, or that only mirrors the letters left to right without turning them upside down, or that changes a digit of the year in a way a genuine turn would not produce, fails this filter.
Step 4: Only one choice survives.
Only pattern R keeps both effects consistent with the example: "Aptitude Test" on top, "GATE - 2026" below it, and every character genuinely turned through $180^{\circ}$.
\[ \boxed{\text{Pattern R}} \]