How to get client machine time zone?

Use JavaScript getTimezoneOffset() Method.  It will return the timezone difference between UTC and Local Time, in minutes. For example, If your time zone is GMT+2, -120 will be returned.

var d = new Date();
var n = d.getTimezoneOffset();

Note: The returned value is not a constant, because of the practice of using Daylight Saving Time.
Tip: The Universal Coordinated Time (UTC) is the time set by the World Time Standard.

Do following in client side on page load:

$(document).ready(function () {
    var d = new Date();
    var tZOffset = d.getTimezoneOffset();
    $.ajax({
        url: '/mytimezone/sendTimezoneOffset',
        data: { timezoneOffset: tZOffset },
        dataType: "json",
        success: function (data) {
           console.log(data);
        },
        error: ajaxErrorCallBack
    });
});

On server side calculate the timezone on the basis of offset:

public ActionResult sendTimezoneOffset(double timezoneOffset)
{
    var zone = TimeZoneInfo.GetSystemTimeZones().FirstOrDefault(x => x.BaseUtcOffset.TotalMinutes == -timezoneOffset);
    string timeZoneId;
    if (zone != null && !string.IsNullOrEmpty(zone.Id))
    {
        timeZoneId = zone.Id;
    }
    return Json(timeZoneId);
}