Final answer:
The sewing technique specifically used to attach hair extensions is known as weaving.
Step-by-step explanation:
The method used to secure hair extensions to the client's hair by sewing is known as weaving. This technique involves creating a braid or cornrow along the client's scalp and then using a needle and thread to sew the weft, or track, of the hair extension into the braid.
Unlike methods like fusion, which uses adhesives, or braiding and sewing, which have their own definitions within hair styling practices, weaving is distinct in its incorporation of sewing to attach hair extensions.