Understand the Clock's Error:

• The clock gains 10 minutes every 24 hours.

Calculate the Total Time Elapsed:

• From 8:00 a.m. on Monday to 6:00 p.m. on Wednesday is 2 days and 10 hours.
• Convert this to hours: 2 days $\times$ 24 hours/day = 48 hours.
• Add the extra 10 hours: 48 hours + 10 hours = 58 hours.

Determine the Clock's Gain in 58 Hours:

• The clock gains 10 minutes every 24 hours.
• In 58 hours, the gain is: $(58 \text{ hours } / 24 \text{ hours}) \times 10 \text{ minutes} = 24.17 \text{ minutes}$.

Calculate the Correct Time:

• The faulty clock shows 6:00 p.m.
• Subtract the gain of 24.17 minutes: 6:00 p.m. - 24.17 minutes $\approx$ 5:35 p.m.

Round to the Nearest Minute:

• Rounding 5:35 p.m. to the nearest minute gives 5:36 p.m.

Therefore, the correct time when the faulty clock shows 6:00 p.m. on Wednesday is approximately 5:36 p.m.