I am assuming you are working from the English pattern for a treble (double in US terms).
For tr3tog you work the treble as usual except that you don’t do the final yo pull through as you work each stitch. You end up with four stitches on the hook including the one that was on the hook before you started to work the tr3tog. Then you yo and pull the yarn through all four.
If you look at the chart below the instructions for Round 12 it does make it clearer where you have to work. It’s on page seven.
It says: Use this chart to work Rounds 11–12 working behind the 5ch-chain loops worked on Round 10.
You can see that Round 11 is shown in black and Round 12 in grey. Rounds 9 and 10 are in blue.
Look for the black dot at the top of the chart which is the start of the Round 12. Can you see what looks like a seed with two lines through? That’s tr2tog. And what looks like a coffee bean with three lines through. That’s tr3tog. The symbols are explained at the side.
You need to join the new yarn into one of the 5 chain loops from Round 10.
Work ch1, ch2, tr2tog (counts as tr3tog). Then ch3 and another tr3tog, ch3, tr3tog.
Where to next?
Underneath the left hand tr3tog “coffee bean” you can see the start of three dc from the previous round where you worked 3 dc, ch4, dc, ch4, 3dc. The dc look like crosses.
You are going to skip the first one of those 3dc, work a dc into the middle one and ch1 over the third.
The pattern is dc, ch1, *dc, ch2, dc ch2, dc, ch2, dc, ch1, dc. What you are doing from * is working dc, 2ch, dc into the 4ch of Round 11 (which were worked into the 5 ch loops of Round 9).
When you get to the end of the section you skip the last of the dcs in the group of three.
Now you are at another 5 ch loop from Round 10 where you repeat tr3tog, ch3, tr2tog, ch3, tr3 tog.
When you get to the end of the round you will work the final dc into the middle dc of the final three dc from Round 11 skipping the last one.
That’s why I asked if you can read a chart. If you can learn how to do this it will make it a lot easier to follow the pattern.
I hope that helps rather than confuse you more.