This site is have an beatiful anime style: Tofugu.com
Anyone know what is the software to draw this anime style?
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Actually the software is mostly independent of the style. The style depent on how the artist is drawing it...
Anyway it is not always possible to redraw a image because the software is not supporting some functions! The style from the website you linked is pretty simple so you do not need something special.
It would be possible to draw the image above with the standard paint of windows except the cheeks (if you look closely a special brush was used to draw this). But this is absolutely not suggested if you really want to redraw it.
The image is very likly drawn with a tablet that supports pressure/speed recognition (recognizable at the fading outlines) and a software that supports paint application modes (recognizable at the shadows/lightning) and also layer support (the green/yellow background is one layer and the girl with the table and the chair is at least one layer).
Such things are mostly supported on a reasonably good painting software: