master.xml

<data>
    <products-by-instances>
        <entry id="1975">
            <name>Sample Name</name>
            <brand>
                <item id="1970">Sample Brand</item>
            </brand>
            <instances>
                <item id="1972">MILT501</item>
                <item id="1974">MILT502</item>
            </instances>
        </entry>
    </products-by-instances>
    <shopping-cart items="2" total="35">
        <item id="1972" num="1" sum="5" />
        <item id="1974" num="3" sum="30" />
    </shopping-cart>
</data>

master.xsl

<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">

<xsl:key name="products-by-instance-id" match="/data/products-by-instances/entry" use="instances/item/@id"/>

<!-- other templates redacted for brevity; the below template is being applied -->

<xsl:template match="/data/shopping-cart/item">
    <xsl:value-of select="key(products-by-instance-id, @id)/brand/item"/>
    <!-- desired output is "Sample Brand" -->
</xsl:template>