@Lakshman 

Below worked for me:

1) If start date is 22nd July then adding 6months to that is 22nd Jan

2) Now it depends on how 6 months you consider since some months are having 30 and 31 days.

3) I would request to check with business for exact days and that would be better.

a) So if user gives 23rd Jan then it gives alert and clears as it is not valid

b) If user gives 22nd Jan then it is ok

Client Script:

Note: Ensure you give valid variable names for start and end dates

function onChange(control, oldValue, newValue, isLoading) {
	if (isLoading || newValue == '') {
		return;
	}

	var ga = new GlideAjax('DateTimeAjax');
	ga.addParam('sysparm_name', "compareDates");
	ga.addParam('sysparm_start', g_form.getValue('start_date')); // start variable
	ga.addParam('sysparm_end', g_form.getValue('end_date')); // end variable
	ga.getXMLAnswer(function(answer){
		if(answer != ''){
                        alert('End date should be within 6 months from start date');
			g_form.clearValue('end');	
		}
	});
	//Type appropriate comment here, and begin script below

}

Script Include: It should be client callable

var DateTimeAjax = Class.create();
DateTimeAjax.prototype = Object.extendsObject(AbstractAjaxProcessor, {

	compareDates: function(){

		var start = new GlideDateTime(this.getParameter('sysparm_start'));
		var end = new GlideDateTime(this.getParameter('sysparm_end'));
		start.addMonthsUTC(6);

		if(end.getNumericValue() > start.getNumericValue()){
			return 'End Date should be withing 6 months from start';
		}
		return '';
	},

	type: 'DateTimeAjax'
});

Output:

Regards
Ankur