You can do it using image_tag
helper:
<%= link_to post, method: :delete, data: {confirm: 'Are you sure?'} do %>
<%= image_tag(your_image_url) %>
<% end %>
or, if you want to do it in one line:
<%= link_to image_tag(your_image_url), post, method: :delete, {confirm: 'Are you sure?'} %>
About your issue with path, since your image file seems to be placed in proper assets directory, this should work:
<%= link_to post, method: :delete, data: {confirm: 'Are you sure?'} do %>
<%= image_tag('x_small_icon') %>
<% end %>