Gosh, these are really fiddly twisted crosses! Most videos show how to do this by reorienting the stitches before working them. The pictures don’t really help do they!
So, for the first set ( left twist), you are starting the manoeuvre at the twisted knit column (it looks like a twisted knit cable on a reverse stocking stitch background? ) Your yarn will already be to the front. Insert your right needle purlwise into your second stitch on the left needle, approaching from behind the first stitch. Now, gently pull this loop to the right of the first stitch ( use your left finger tips on the left needle to stop the first 2 stitches flipping off the needle!) Then purl the loop ( which also stays on the left needle as it is still held there by the first stitch ). Make sure that you don’t also make a yarn over whilst purling.
The pictures don’t show this pulling step but you need to get the second stitch to the right of the first to stop the loops in front of the first stitch which are shown in step 2. Then knit the first stitch on the right needle tbl. You then drop both stitches off the left needle as both have been secured. You need to have a fairly firm tension in this manoeuvre as it can get a bit sloppy, or tighten up after you’ve dropped the left needle stitches.
The right twist is much easier! This time, you start the manoeuvre one stitch before the knit column. Move your yarn to the back. Knit the second stitch on the left needle tbl (keeping it on the needle and watch your tension isn’t too loose!) Then move your yarn forward and purl the first stitch on the needle and drop both.
Have a go on a swatch first!! The pictures are misleading. What a shame! Good luck - out makes a lovely pattern!