Responsive grid in view layout
The important thing to make this work is the theme that your using; the Views Responsive Grid doesn't do much by itself with regards to styling but it allows you setup you view to apply the appropriate CSS class from your theme to make your display responsive. 

You are using the Corporate Clean theme but it's not a truly responsive theme from what I can see from its layout CSS. You can still have that layout that you want for one screen type so that will be what I will show you here.


Change your view's format to Responsive Grid

Next change the settings for the Responsive Grid format to have  2 column in horizontal alignment and the class grid_6 to every column. You can also use grid_4 if you have a sidebar on your page.

Then change the Format's Show options to fields.


Now in the fields section add all the fields that you want to display. For example, I have the fields title, body and post date.



The next step requires you to add some custom html/css; normally advanced view display formats such as Views Bootstrap would have different options to display your fields. For example, had you been using a Bootstrap based theme the Media Object format would have served you well. 

However, since you are using something different, I would recommend you override the out of the fields as follows.


Hide all but the last one of your fields by clicking on each field and checking the "Exclude from display option". 

For the last field override its display by clicking on it and going to the Rewrite Results section. In the text box provided add in your custom HTML markup with along your fields using tokens provided by views.

In you theme make sure to add proper CSS classes, i.e, in the example HMTL I'm showing you should have the classes clinic, clinic-thumb and clinic-details. These should have the styling in such a ways that the clinic class clear floats, the clinic-thumb and clinic-details classes should have floats and respective widths. 
Example CSS:

/**


.clinic has a clearfix taken from this page 
*/


.clinic:before,
.clinic:after {
    content: " "; /* 1 /
    display: table; / 2 */
}
.clinic:after {
    clear: both;
}
/**


For IE 6/7 only
*/
.clinic {
*zoom: 1;
}


.clinic-thumb{
 width: 35%;
 padding-right: 5%;
 float: left;
}
.clinic-details{
 float: left;
 width: 60%;
}


If you followed my example you should get something like this:



Hope this helps!