The average collection period is the average number of days it takes for a company to collect payment from its customers after a sale has been made. In this case, XYZ Ltd. extends credit terms of 45 days to its customers. This means that customers have 45 days from the date of the sale to make payment.

To determine if XYZ Ltd.'s credit collection is poor, we need to compare the average collection period to the credit terms. If the average collection period is longer than the credit terms, it indicates that customers are taking longer to make payment than they are supposed to, which can be a sign of poor credit collection.

Let's analyze each option:

a) 30 days: If the average collection period is 30 days, it means that, on average, customers are making payment within 30 days of the sale. This is shorter than the credit terms of 45 days, so it would not be considered poor credit collection.

b) 36 days: If the average collection period is 36 days, it means that, on average, customers are making payment within 36 days of the sale. This is also shorter than the credit terms of 45 days, so it would not be considered poor credit collection.

c) 47 days: If the average collection period is 47 days, it means that, on average, customers are taking 47 days to make payment after the sale. This is longer than the credit terms of 45 days, so it would be considered poor credit collection.

d) 37 days: If the average collection period is 37 days, it means that, on average, customers are making payment within 37 days of the sale. This is shorter than the credit terms of 45 days, so it would not be considered poor credit collection.

Therefore, the correct answer is option 'C' (47 days), as it represents an average collection period that is longer than the credit terms, indicating poor credit collection.