Magento : Display all products with their Categories on Home Page -

i need display products assigned categories on home page of website below.

category      category b      category c           ----------      -----------     ----------               product       product b       product c 

in cms > home page > content section have included block

{{block type="catalog/product_list" name="homeproduct_list" template="catalog/product/list.phtml"}} 

here catalog/product/list.phtml default magento list.phtml without modifications.

my products displayed on home page if assign product category default category (root category)

for ex: product assigned default category (root) , categopry 

if assign product category (which want) not show products on home page.

the issue here not 1 how display products in homepage? why have assign product default category (root) in order display on home page.

thanks.

because when have database table catalog_category_entity store category id first must root category/subcategory/subcategory[if] , when fetch so,you have first must assign root category subcategory

$product->getcategoryids() category id please check image