To calculate the number of sets of 10 headsets the distributor must order for the manufacturer to break even, we need to set up an equation to find the break-even point.

Let's define x as the number of sets of 10 headsets ordered by the distributor.

Total cost for the manufacturer per set of 10 headsets:
Manufacturing cost per set + Packaging and shipping cost per set
= $13.39 + ($12.00 / 10) = $13.39 + $1.20 = $14.59

Total revenue for the manufacturer per set of 10 headsets:
Selling price per set = $18.25

Now, we can set up the break-even equation:

Total revenue = Total cost + Fixed costs
18.25x = 14.59x + 2000 + 75

Solving for x:

18.25x - 14.59x = 2075
3.66x = 2075
x = 2075 / 3.66
x 567.21

Since the distributor cannot order a fraction of a set, they need to order at least 568 sets of 10 headsets to reach the break-even point for the manufacturer.