General Request - i want this style
 

Please does anyone know the name of the style that carries this photo on the banner

Impossible to tell from a banner. Just look at the bottom of the forum or ask the owner of the forum. If there's no indication that they used a public style, it's probably unique and not available to download.

This forum was mine for a long time, the banner came along with the style, but I forgot the name of the style, if I'm not mistaken it's from 2013, I can't find it anymore

Could it be the "Ambient" style? It looked like this and it seems to match the colors of the banner.

https://vborg.vbsupport.ru/external/2019/08/1.png

yes it is this skin! but i would like banner which came along with the hooded man

I believe it was a style created/sold by vbskin.net but they do no longer exist. I wouldn't know where you can download it but maybe if you Google properly, you can find it somewhere. I don't think it came with the banner you showed though, it was most likely added by someone else.

It was a skin called Ambient Lighting Skin, it was available here, but it was removed by op.

Apparently it was a Joomla skin that they (vbskin.net) converted to vBulletin without the permission of the original owner and therefore it had to be deleted. You can find the original Joomla skin here https://joomla.carbonmade.com/projects/2266059

I knew this style, this is a style pretty old that it is used by many forums in many years ago. Honestly the official style of it looks more better than your image.