Help overriding CSS stylesheet style

Greetings.  I am adding one section onto a website that is already in existence.  I do not want to modify any of the .CSS sheets that are in the main site, but I have linked to them so that I can benefit from the same styles.

However, in some situations I want to override these .css styles from the root site.   For instance, I want the text size (defined in the p tag on the main site) to be 12, but in the main root site, the size is 14.  No matter what I try, I can't seem to override this style.  I have a stylesheet used only in my section of the site, and when I try and redefine the <p> tag in this sheet, it continues to be overruled by the main sheet.  

Are there ideas of how I can best overrule the style?  At this point, I'm not concerned with best practices, but simply want this to work.  Thank you.