var xdoc = XDocument.Load(path_to_xml);
var result = xdoc.Root.Elements("b")
.Where(b => (string)b.Attribute("id") == "r4")
.SelectMany(b => b.Element("P").Elements("Pr"))
.Select(pr => (string)pr.Attribute("id"));
Or with XPath:
var result = xdoc.XPathSelectElements("a/b[@id='r4']/P/Pr")
.Select(pr => (string)pr.Attribute("id"));