I am wondering if it is possible to move the image on the for each children category and the items in it to the left of the description instead of it being on top? Can any one explain this to me? Please see picture attachment below.

Also can anyone help me to remove the word Children Categories? I have tried everything that I have read on this board but it is not removing. Please help me this is the only things that are holding me up on this site.

you can edit the layout of category blog view, or item views by creating a custom template.

go here:
components/com_k2/templates

copy the default template folder to a new template name.

edit those files as desired.

assign the category to the template in the Category item layout panel.

to edit children categories you can edit
language/en-GB/en-GB.com_k2.ini

that is unless your language is something other than english.