A DST file is the result of digitizing a design for embroidery. That is to say, a digitizer takes a graphic (such as a jepg), and creates a file that gives sewing instructions to the embroidery machine.
This is not a matter of simply converting from one file format to another. It requires specialized skills of a digitizer.
The embroiderer should be able to create the file for you. I would expect the cost to be at least $45. Cost usually depends on the number of stitches, colors, and the size and complexity of the design.
It's in your best interest to have the person who will be embroidering the item do the digitizing. If the embroiderer is not capable of digitizing the graphic, or does not have a resource to sub contract it out, then I'm afraid they probably aren't very experienced.
If having your own design digitized is beyond your budget, then consider using a stock design provided by your embroiderer, or plain text.
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