Edit in JSFiddle

function ViewModel() {
    var self = this;
    self.technique = ko.observable("");
    self.technique.subscribe(function (newValue) {
        self.techniqueText($("input[name=aspnet]:checked").next().text());
    });
    self.techniqueText = ko.observable("");
}

ko.applyBindings(new ViewModel());

<label>
    <input name="aspnet" type="radio" value="webforms" data-bind="checked: technique" /><span>ASP.NET Web Form</span></label>
<label>
    <input name="aspnet" type="radio" value="mvc" data-bind="checked: technique" /><span>ASP.NET MVC</span>
</label>
<label>
    <input name="aspnet" type="radio" value="webapi" data-bind="checked: technique" /><span>ASP.NET Web API</span>
</label>
<div data-bind="text: techniqueText"></div>