Monkey and Dog compatibility
Monkey (Shen, 申) and Dog (Xu, 戌): no named relation.
These are fixed relations among the twelve branches of the Chinese calendar, set out in the classic San Ming Tong Hui (三命通会), written in 1578, quoted below. They describe the signs, not two people: no classic gives a method for matching two people by their signs, so there is no score here.
What the book says
Monkey and Dog have none of the relations: no harmony, clash, punishment, harm or break. The book has nothing to say about this pair in particular.
Their elements
The Monkey is Metal and the Dog is Earth: Earth feeds Metal.
San Ming Tong Hui’s section on the zodiac animals happens to name these two. It gives the element reasoning, and then asks why the real animals do not behave that way:
The monkey is afraid of the rat, and what bites the monkey is the dog. The rat is Water and the monkey Metal; Water does not overcome Metal, so why does the monkey fear the rat? The Dog is Earth and the Monkey the monkey; Earth does not overcome Metal, so why does the monkey fear the dog?
猕猴,畏鼠者也,啮猕猴者,犬也。鼠,水,猕猴,金也,水不胜金,猕猴何故畏鼠?戌,土也,申,猴也,土不胜金,猴何故畏犬?
Matched by how their elements overcome each other, the creatures of the twelve branches do not correspond at all. Wherever blooded creatures master one another, even to eating one another, it comes down to sharp or blunt teeth and strong or weak sinews.
十二辰之禽以气性相克则尤不相应。大凡含血之虫相服,至于相啖食者,以齿牙钝利、筋力优劣自相胜服也。
San Ming Tong Hui, volume 2: On the animals of the branches (论地支属相) · source text
How much it counts
A sign is one character of the eight in a BaZi chart, the year’s branch. The book reads these relations between the pillars of one chart, and tells the reader to look at the whole chart’s elements first:
Clash and break, three harmony and six harmony: where a chart has them, ask next how its five elements get on. Misfortune may give rise to blessing, and blessing to misfortune.
相冲相破,三合六合,命中有之,即求五行相得何如。或祸中生福,福中生祸
San Ming Tong Hui, volume 3: On the symbolic stars as a whole (总论诸神煞) · source text
Birth years, and 2027
- Monkey: 1932, 1944, 1956, 1968, 1980, 1992, 2004, 2016. In 2027, the Year of the Fire Goat (Ding Wei, 丁未), the Monkey has no clash with the year.
- Dog: 1934, 1946, 1958, 1970, 1982, 1994, 2006, 2018. In 2027, the Year of the Fire Goat (Ding Wei, 丁未), the Dog is punished by the year (Xing Tai Sui, 刑太岁) and breaks with the year (Po Tai Sui, 破太岁).
A sign’s year is usually counted from Chinese New Year, between late January and mid-February; BaZi counts it from the Start of Spring, about 4 February. Born in January or early February? You may be the sign before: the sign pages check your date.
Two real people?
Each person’s chart has eight characters, and the same relations run between all of them, not only the two signs. The two-chart page sets both charts side by side, branch by branch, and gives what each chart says about marriage on its own. No score there either.
Monkey with the other signs: Rat · Ox · Tiger · Rabbit · Dragon · Snake · Horse · Goat · Monkey · Rooster · Pig.
Dog with the other signs: Rat · Ox · Tiger · Rabbit · Dragon · Snake · Horse · Goat · Rooster · Dog · Pig.