Hello Katerina - took me a while before I would pluck up courage to swap to linen and working over two, so well done. I think the half cross stitches that are being referred to in this section are the horizontal and vertical stitches seen more regularly these days on charts. I vaguely recall reading somewhere that this particular type of stitch had all but disappeared until the Royal School of Needlework started to promote the re-introduction of them. I think too this is where the mix up has occurred elsewhere on the forum as to the term 'half cross stitches'
If you think of stitching on say 28 count and you are doing a vertical half cross stitch you stitch up or down over two but across by only one (that's where the 'half' bit comes in)- but still do it as if doing a full crossed-stitch. Similarly if doing a horizontal half cross stitch you stitch up or down over one but across by two.
As a consequence you end up with either a tall but squashed looking stitch (the vertical) or a flat (on its back) but squashed stitch - the horizontal. There are several charts out there now with these two stitches in and having helped out two ladies who couldn't get to grips with the stitch I can tell you that they do look very effective.
It's always difficult trying to explain these things in print - so much easier if you can just see it as a large diagram. I've just read this through and find it difficult to understand - yet I can do the flipping stitches! I think I shall do a few on a bit of fabric and bring it to Bradford then if there's anybody there who wants to have a look, they can. Just remember - stitching is for enjoyment so don't go tearing your hair out in frustration. Brenda