K3tog with Gtog came up when I needed to decrease stitches and one of the stitches was a k1-GSR from the previous German short row. Doing a k3tog with Gtog allows the k3tog to be done, while also closing up that k1-GSR.
How to do a k3tog with Gtog
With the right needle, as to knit, go into the 3rd stitch, the 2nd stitch, and then into both legs of the k1-GSR of the 1st stitch on the left needle. Knit 3 together (or if you are counting both legs of the k1-GSR, knit 4 legs together). Decreases 2 sts.
What is a Gtog?
When the stitch is pulled over the needle when working a k1-GSR or p1-GSR there are two legs to the stitch that was pulled. To close the short row, those two legs are either knit together, or purled together into 1 stitch. I use Gtog because it can be either a knit 2 together or a purl 2 together, depending on how the stitch is to be worked in pattern. It is a k/p-2tog, but not two separate stitches, rather, 2 legs of a single stitch.
The k3tog with Gtog is used in Belon where there are stitches still remaining to be decreased after working the Dec12 on the previous row. The extra two stitches need to be eliminated before beginning the next repeat of the stitch pattern and this is the last row of the repeat.
See also: German Short Rows, GSR & Gtog