Hi,
Please go to the CMS >> Page, chose the page with title ‘Lunar Home page’, url key ‘lunar_home_page’. Find the code bellow:

<block type="core/template" template="sns/blocks/tabs.phtml" name="tabs.slider">
	<action method="setTitle"><title>New Product</title></action>
	<block type="products/slider" name="slider_tab1">
		<action method="setConfig">
			<name>
				<title>Men</title>
			</name>
		</action>
		<action method="addToParentGroup"><group>custom_tabs</group></action>
	</block>
	<block type="products/slider" name="slider_tab2">
		<action method="setConfig">
			<name>
				<title>Women</title>
			</name>
		</action>
		<action method="addToParentGroup"><group>custom_tabs</group></action>
	</block>
	<block type="products/slider" name="slider_tab3">
		<action method="setConfig">
			<name>
				<title>Child</title>
			</name>
		</action>
		<action method="addToParentGroup"><group>custom_tabs</group></action>
	</block>
</block>

You can add the code ‘<product_category>ID</product_category>’ into the tags ‘<name></name>’ , with ID is the same category’id. For example: 1, 2.. This to show the products on categories right.
And you can custom the title of categories by changing the tags ‘<title></tile>’
You can custom like that,

<block type="core/template" template="sns/blocks/tabs.phtml" name="tabs.slider">
	<action method="setTitle"><title>New Product</title></action>
	<block type="products/slider" name="slider_tab1">
		<action method="setConfig">
			<name>
				<title>Men</title>
				<product_category>39</product_category>
			</name>
		</action>
		<action method="addToParentGroup"><group>custom_tabs</group></action>
	</block>
	<block type="products/slider" name="slider_tab2">
		<action method="setConfig">
			<name>
				<title>Women</title>
				<product_category>81</product_category>
			</name>
		</action>
		<action method="addToParentGroup"><group>custom_tabs</group></action>
	</block>
	<block type="products/slider" name="slider_tab3">
		<action method="setConfig">
			<name>
				<title>Accessories</title>
				<product_category>79</product_category>
			</name>
		</action>
		<action method="addToParentGroup"><group>custom_tabs</group></action>
	</block>
</block>

Thanks,