- For Teachers
Like bhaisahab I would probably say "double sink", but Google-ing "double sink image" and "twin sink image" not only shows numerous examples of the same type of sink but many of the very same images. There may be regional differences but I think that both terms would be widely understood as meaning the type you have pictured.
not a teacher
Also, bear in mind that the two images shown in the Original Post show different things. The right-hand image shows two equally-sized sinks side by side. I'd call that 'a double sink'. The left-hand image shows a more limited/less flexible arrangement; you can't use the little sink in the same way as the main sink. It's a cheaper way of producing something that people want, to "keep up with the Jones's" without paying for a double one. I'd call that a 'twin sink'. (But individual manufacturers/catalogues might differ, and I'm not terribly confident about the distinction - which I rarely have occasion to make in real life. And of course this might be a case of that tendency that 5jj mentioned elsewhere, for ELT professionals [and other language introspectors] to invent tempting but unreal distinctions.)
If the two sinks are of equal size, I would call it a double sink. With the other style, where there is a normal size sink and then a smaller one to the side, I don't think I have ever heard a specific name. As you can see from this DIY store website description, the main title only refers to it as a"Cooke & Lewis Axin 1.5 Sahara Beige Bowl Sink"
but the longer description explains that the unit also has a "half bowl" which could be used as a waste disposal unit (garbage disposal in the US, I believe) or as a food preparation area.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.