Adding/substracting days in Shopify's Liquid template language

snippet.liquid

{% assign days = 4 %}

{% assign ms = days | times: 24 | times: 60 | times: 60 %}
{% assign now = 'now' | date: "%s" %}

{% assign today = now | date: "%b %d" %}
{% assign before = now | minus: ms |date: "%b %d" %}
{% assign after = now | plus: ms | date: "%b %d" %}

<div>Today: {{ today }}</div>
<div>{{days}} days before today: {{ before }}</div>
<div>{{days}} days after today: {{ after }}</div>

Result:

<!-- HTML -->
Today: Aug 29
4 days before today: Aug 25
4 days after today: Sep 02

Explaination:

First convert now to seconds since 1970 with filter | date: "%s".
Convert days range to seconds x 24 x 60 x 60
Use filters | minus or | plus to get the result and parse back to date format with date: "%b %d" filter

The format for Liquid date is the same as strftime