Given this folder structure,
YourProject
 |-- src
 |    `-- com
 |         `-- example
 |              `-- BackingBean.java
 |-- WebContent
 |    |-- META-INF
 |    |-- WEB-INF
 |    |-- resources
 |    |    `-- icons
 |    |         `-- foo.png
 |    `-- foo.xhtml
 :
You can get it by either ExternalContext#getResourceAsStream() which takes webcontent-relative path:
ExternalContext externalContext = FacesContext.getCurrentInstance().getExternalContext();
InputStream input = externalContext.getResourceAsStream("/resources/icons/foo.png");
// ...
Or by Resource#getInputStream() wherein Resource is obtained from ResourceHandler#createResource() which takes a /resources-relative path:
ResourceHandler resourceHandler = FacesContext.getCurrentInstance().getApplication().getResourceHandler();
InputStream input = resourceHandler.createResource("icons/foo.png").getInputStream();
// ...
As to selecting the image and passing its path around, just do something like as follows:
<h:graphicImage name="icons/foo.png">
    <f:ajax event="click" listener="#{bean.setImage(component.name)}" />
</h:graphicImage>
<h:graphicImage name="icons/bar.png">
    <f:ajax event="click" listener="#{bean.setImage(component.name)}" />
</h:graphicImage>
<h:commandButton value="submit" action="#{bean.saveImage}" />
See also: