show products of a category on home page in magento 1.9.2.2

After last patch, SUPEE-6788, Magento includes a white list of allowed blocks or directives. If a module or extension uses variables like {{config path="web/unsecure/base_url"}} and {{block type="catalog/product_list"}} in CMS pages or emails, and the directives are not on this list, you will need to add them with your database installation script.

You can configure allowed variables and blocks in System > Permissions > Blocks and System > Permissions > Variables.

SUPEE-6788 complete details: http://magento.com/security/patches/supee-6788-technical-details

Due SUPEE-6788 patten,you can use below:

As alternative solution.

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goto Design tab of Your cms page

Put below layout xml code at Layout Update XML field

<reference name="content">
<block type="catalog/product_list" name="home.catalog.product.list" category_id="7" template="catalog/product/list.phtml" />
</reference>

It will not create issue in permission