Yours is at least the third question here about "how do I connect the Dot audio to my stereo receiver". It's beginning to make me feel like I am back working in the stereo store from my past days and answering "Stereo 101" questions from customers again. I hope you saw the other similar questions posted here.
Anyway, your question is different enough, so I will tackle it.
First, the output of a Dot is a high-level signal as one from most gadgets are (except for Phono outputs which are low-level ones and MUST be plugged in to an amp's Phono input (and nothing else). NEVER plug anything into phono input other than a turntable output.
So, pretty much all the other inputs are high-level, (unless the amp has a mic in, and many amps do not have this input -- but keep away from this one, too).
OK, from your photo I don't see too many spare inputs, but you may be able to use an unused DVD input (or other) of receiver if:
-- all the HDMI cables (from gear) are plugged into the TV's HDMI ports and audio of these devices play through the TV speakers -OR- from TV into another device such as a soundbar.
-- BUT, if any of the audio of these devices (especially the DVD player) are plugged into the receiver, you CANNOT use the DVD (or other) input of receiver; for if you do, you would be putting two signals into the same circuit -- not good.
A key question: What audio outputs from which devices do you have plugged into your receiver, and what devices are plugged into your TV via HDMI, and either play their audio via TV speakers (or a soundbar)?
Now, regarding the cabling needed. There are nice cables made with a 3.5 male plug on one end and red and white RCA plugs for L/R on the other end; they are about 3 feet long. I have a few of them in use. This is what you need to connect the Dot to the receiver. If you need more cable, there are stereo extension cables that have a male 3.5 plug on one end and a female plug on the other end. Be sure you get a STEREO variety of this cable; the shorter the better to reduce signal loss. A 20 foot cable would likely be the max, but if a 10 foot cable can do the job, get it.
Once you answer the above questions we can probably wrap this up.