The mistake was that 12² was calculated incorrectly. 12² means '12 squared', which is 12 × 12. Of course, 12 × 12 is 144, but the student worked out 12 × 2, which is 24.
Therefore, to work out the correct answer, the student has to replace 24 with 144 and continue to work out the answer:
A = πr²
A = 3.14 · 12²
A = 3.14 · 144
A = 452.16 yd²