How to handle field with multiple items
The standard field handler in Views returns flat rendered output. To change this or put in the feature for even/odd numbered values you would need to implement a field handler plugin. For this task that would be a bit too much work. You can improvise in theming to get the same result.

In Views you can define a separator for multiple field values. Choose a separator that is not in the content of the field. Default is ','.

In Twig you can use the filter split to get the array items. Use the separator from the multiple field settings.

views-view-field--field-fieldname.html.twig

{% set items = output|split(',') %}


Put items in a loop and display only even number items:

{% for item in items %}
  {% if loop.index is even %}
    {{ item }}
  {% endif %}
{% endfor %}