Step 1: Cotton Count.
Cotton count is defined as the number of hanks of 840 yards that weigh one pound.
Thus, Cotton Count → II.
Step 2: Tex System.
Tex is the weight in grams of 1000 meters of yarn.
Thus, Tex → III.
Step 3: Worsted Count.
Worsted count is based on the number of hanks of 560 yards that weigh one pound.
Thus, Worsted Count → I.
Step 4: Metric Count.
Metric count is defined as the weight in kilograms of 1 km of yarn.
Thus, Metric Count → IV.
Step 5: Conclusion.
Therefore, the correct match is: A - II, B - III, C - I, D - IV.