Displaying Sub Categories on Category Page
It's hard to figure out exactly what your trying to do, but I can see a few potential problems.


No need for the 'num' variable, instead use loop.index (or loop.index0 for a zero indexed array); although I don't think you need it at all in this case.
nth() is currently returning the 'nth' offset of all assets that are related to all children collectively (thus the strange results). I would guess that you want the asset(s) related to the child category in the current loop. I would also guess that the asset(s) are defined in an assets field in the categories field layout, in which case you can get the asset(s) from the field directly, rather than using .relatedto(child).


Try the following — without understanding your structure entirely, it might at least be a bit closer to what you're looking for.

{% if category.hasDescendants() %}

    {% for childCategory in category.getDescendants() %}

        &lt;div id="teaser" class="row"&gt;

            &lt;div id="teaser_image" class="columns left small-12 medium-6"&gt;

                {% set asset = childCategory.myAssetsFieldHandle.first %}
                {% if asset %}
                    &lt;img src="{{ asset.url }}" alt="{{ asset.title }}"&gt;
                {% endif %}

            &lt;/div&gt;     

            &lt;div id="teaser_text" class="columns right small-12 medium-6"&gt;
                &lt;h2&gt;{{ childCategory.title }}&lt;/h2&gt;
                &lt;p&gt;{{ childCategory.description }}&lt;/p&gt;
            &lt;/div&gt;

        &lt;/div&gt;

    {% endfor %}

{% endif %}

&lt;div id="teaser" class="row"&gt;

    &lt;div id="teaser_image" class="columns left small-12 medium-6"&gt;
        &lt;img src="/images/moses-har-sinai.jpg" alt=""&gt;
    &lt;/div&gt;

    &lt;div id="teaser_text" class="columns right small-12 medium-6"&gt;

        {% set entries = craft.entries.relatedTo(category) %}
        {% for entry in entries %}
            &lt;h2&gt;{{ entry.title }}&lt;/h2&gt;
            &lt;p&gt;{{ entry.description }}&lt;/p&gt;
            &lt;a class="button small" href="{{ entry.url }}"&gt;Learn more&lt;/a&gt;
        {% endfor %}

    &lt;/div&gt;

&lt;/div&gt;


Note: this is assuming that you want to show the subcategories and then the entries related to the main category. If not, then I misinterpreted your question and you will want to reconfigure this a bit, but the principles should be the same.