The categories and the tags come as one section. You can move the section with a snippet in functions.php of your child theme:
remove_action( 'woocommerce_single_product_summary', 'woocommerce_template_single_meta', 40 );
add_action( 'woocommerce_after_single_product_summary', 'woocommerce_template_single_meta', 5 );
Then tidy it up with:
.product_meta {
clear: both;
}
.sku_wrapper,
.posted_id,
.tagged_as {
display: block;
}
.tagged_as {
visibility: hidden;
height: 120px;
}
.tagged_as:before {
content: "Etiquetas:";
visibility: visible;
}
.tagged_as a {
margin-bottom: -26px;
display: block;
visibility: visible;
}
To move just the tags, you would need to make a new meta template.
Copy
wp-content/plugins/woocommerce/templates/single-product/meta.php
to
wp-content/themes/<your-child-theme-name>/woocommerce/single-product/meta.php
and remove the tags line 36 from the copy of meta.php.
Next, use the add_action() similar to above to insert a new function to print just the tags.
That’s a bit more code than would normally be provided as a forum answer. PHP skills or a developer would be needed.