How was the position of Gods determined? For example, why is Shiva shown between the eyebrows? Why are Bhairava and Hanuman shown in the legs?
Well, we can't be sure if the painter of the picture in question is well versed in Scriptures or that he has drawn the positions of various Gods exactly as depicted in our Shastaras.
However,one can get a good summary of the positions of Gods,Rishis,Vedas etc in a Cow's body in the "Grihasta Ashrama" chapter found in the Skanda Purana.
In the Grihashtashram (family life), Maharshi Veda Vyas extolled to Yudhishthar the virtues of human beings, especially Brahmanas, as they play a pivotal role in performing duties to Devas, Pitras, Co- human beings, Bhuta Pranis, Krumi-Keetas (insects), Pakshis (birds) and even Asuras.
Cows standing for virtues do fall in the care of Brahmanas as the former represent Vedas-Rig Ved being the back of Cows, Yajur Ved being their middle portion, and Sama Ved their ‘Kukshi’(stomach); ‘Ishta’or Yagnas and Yagas and ‘Apurti’ or Wells, Tatakas, Gardens etc are their horns; Veda Suktas are the body hairs; Shanti Karma and Pushti Karma are their dung and urine; ‘Aksharas’ are their feet; Cows live for their Pada-Krama-Jata-and Ghana Paatha viz. the various Mantras; Swahakar, Swadhakar, Vashatkar and Hanthakar are the four nipples of their breasts, each of the nipples representing Devatas; Pitras; Bhutas, Rishis, Munis and Sureswaraganas; and Human beings respectively. The last nipple yeilds maximum milk to human beings.Thus the responsibility of looking after cows is squarely on human beings
Answer for this question is also found in the Padma Purana.
Padma Purana, Srishti Khanda, Chapter 48, Verses 157 to 164:
The Vedas with their six limbs and the pada and krama, reside in the mouth of cow. On the horns Hari and Kesava always stay together.
In the belly lives Skanda; and Brahma always remains in the head. Sankara lives in the forehead and Indra on the tip of the horn.
The deities, Asvins, live in the ears; the Moon and the Sun live in the eyes. God Garuda lives in the teeth, and Sarasvati in the tongue.
All the sacred places remain in the anus, and the Ganges in the urine. The sages live in the pores of the skin, and Yama lives in the backside of the face.
Kubera and Varuna have resorted to the right side; the lustrous and very powerful Yaksas reside in the left side.
Gandharvas reside in the centre of the face, and the serpents on the tip of the nose. The celestial nymphs have resorted to the hind parts of the hoofs.
The all-auspicious LaksmI resides in the cow-dung and cow-urine. Those who move in the sky reside on the tips of the feet; Prajapati lives in the bellowing sound.
The full four oceans reside in the udders of the cows. A mortal who everyday bathes and touches a cow, gets relieved from all major sin