Assuming this is the kind of standard problem:
Imagine the circular city. Divide it into $n$ annuli of very small width, $\Delta r$. The density of population in an annular region is almost constant. If we are $r_i$ away from the center on the inner edge of the annular region, the density is well approximated by $D(r_i) = 20-4r_i$ thousand people per square kilometer. The area of the annular region is also well-approximated by "slicing it open and stretching it out", which will give you a shape that is very close to a rectangle of height $\Delta r$, and of width $2\pi r_i$, so the area is approximately $2\pi r_i\Delta r$ square kilometers. So the population in the annular region just described can be approximated by: $\text{Population in the }i\text{th region}\approx (20-4r_i)(2\pi r_i)\Delta r\text{ thousand people.}$ Adding it up over all the annular regions we have that $\text{Population of the city} \approx \sum_{i=1}^n (20-4r_i)(2\pi r_i)\Delta r.$ If we take the limit as $n\to\infty$, the approximations gets better and better (both the area approximations and the density approximations), and the error goes to zero. So $\text{Population of the city} = \lim_{n\to\infty}\left(\sum_{i=1}^n(20-4r_i)(2\pi r_i)\Delta r\right).$
But these sums are Riemann sums of a particular function, and so the limit will equal an integral. Figure out what integral, and then performing the integration will give you the population.