You could try unravelling the last row before the cable and knit it looser (you can use a larger needle for this specific row).
Also, don’t work the cable stitches tightly.
Try pushing the stitches on the cable needle closer to the tip of the needle.
When knitting the cabled row you could do a left-leaning cable, instead of the right-leaning, maybe this will feel more comfortable: place the first 8 sts on the cable needle and hold the needle to the FRONT of your work. Knit the remaining 8 sts, then knit the 8 sts from the cable needle.

Just wanted to say: I think the folks who are ragging on this pattern are doing so because cabling that many stitches feels really clunky – your yarn will get really tight and the resulting weird little accordion of material you end up with will feel like you did something wrong. Persevere! Once you get a row or two past the cable, things will start to flatten out & make sense again!

The working yarn is connected to the first stitch, so, when you slip the first 8 stitch on a cable needle you bring the yarn forward and knit the 8 stitches left on the needle, then you knit the 8 stitches from the cable needle. It is just as if you are working a cable.

Yes, you do the cable-twist once on the right-side row, and continue knitting in the established pattern.