To estimate the total number of kittens in the city's shelters based on the sample data, we can use the proportion of kittens in the sample.
From the sample of 70 cats, there are 12 kittens.
The proportion of kittens in the sample is: \[ \text{Proportion of Kittens} = \frac{\text{Number of Kittens}}{\text{Total Number of Cats in Sample}} = \frac{12}{70} \]
Now, to estimate the number of kittens in the total population of 2,200 cats, we apply this proportion: \[ \text{Estimated Number of Kittens} = \text{Proportion of Kittens} \times \text{Total Number of Cats} = \frac{12}{70} \times 2200 \]
Calculating this: \[ \text{Estimated Number of Kittens} = \frac{12 \times 2200}{70} = \frac{26400}{70} \approx 377.14 \]
Rounding to the nearest whole number, we find approximately 377 kittens.
Thus, the answer is: 377 cats.