After a 20% discount, the price of a T-shirt was $40. A first-time customer was given a further discount of $6. What was the total percentage discount given to a first-time customer for the T-shirt?

1. Find the original price of the T-shirt before any discount.

The price after a $20\%$ discount is $80\%$ of the original price.
$80\% \rightarrow \char36{}40$
$1\% \rightarrow \char36{}40 \div 80 = \char36{}0.50$
$100\% \rightarrow \char36{}0.50 \times 100 = \char36{}50$
The original price is $\char36{}50$.

2. Calculate the total discount given to the first-time customer.

Initial discount = $\char36{}50 - \char36{}40 = \char36{}10$
Further discount = $\char36{}6$
Total discount = $\char36{}10 + \char36{}6 = \char36{}16$

3. Calculate the total percentage discount.

Total percentage discount = $\frac{\text{Total discount}}{\text{Original price}} \times 100\%$
$= \frac{16}{50} \times 100\%$
$= 32\%$