Sometimes you can't hoop the fabric directly, but taping or pinning doesn't give enough stability to prevent your fabric shifting. Enter the basting box: a stitch that goes around the perimeter of the hoop to tack down the fabric to the stabilizer.
These pre-made basting boxes use a 3mm stitch, so they're very easy to rip out if you're embroidering on a larger piece - the lock stitches at either end will be the hardest bit, but from the stabilizer side it's pretty straightforward. And just advance past them and stop before the ending ones if you think your fabric is likely to give you trouble with those.
None of these basting boxes may look like they fit your machine, but that's because they're the more precise metric versions: my 5x7 machine, for instance, is really 5.11" wide and 7.08" long - 130x180mm. A 4x4 hoop is slightly smaller than 4x4, usually a nice even 100mm square.
If you're using Ink/Stitch (and you should be!), you can even put the hoops in as Inkscape page sizes. There's a pages.csv included - just replace the default one and you can set your page to a standard hoop size at a click. Even if you don't use Ink/Stitch, open up that file to see the metric equivalent for your hoop.
"6x10" can mean either a 150x250mm hoop, or a 160x260mm hoop. Not sure which you have? Try loading the 160x260 basting box and you'll know.
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