How to convert a word file(docx) to pdf using asp.net c#

To my knowledge the only free solution is Microsoft Interop Word with iTextsharp.
Since you don't want to use Microsoft Interop Word, I think you should consider using professional SDK. This code shows how you can convert DOCX to PDF using LEADTOOLS:
/*******************************************/
using Leadtools;
using Leadtools.Codecs;
using Leadtools.Forms.DocumentWriters;
using Leadtools.Svg;
using Leadtools.Documents;
using Leadtools.Caching;
using Leadtools.Annotations.Core;
using Leadtools.Forms.Ocr;
using Leadtools.Documents.Converters;
 
public void DocumentConverterExample()
{
   using (DocumentConverter documentConverter = new DocumentConverter())
   {
      var inFile = @"c:\Leadtools.docx";
      var outFile =@ "c:\output.pdf";
      var format = DocumentFormat.Pdf;
      var jobData = DocumentConverterJobs.CreateJobData(inFile, outFile, format);
      jobData.JobName = "conversion job";
      var job = documentConverter.Jobs.CreateJob(jobData);
      documentConverter.Jobs.RunJob(job);
 
      if (job.Status == DocumentConverterJobStatus.Success)
      {
         Console.WriteLine("Success");
      }
      else
      {
         Console.WriteLine("{0} Errors", job.Status);
         foreach (var error in job.Errors)
         {
            Console.WriteLine("  {0} at {1}: {2}", error.Operation, error.InputDocumentPageNumber, error.Error.Message);
         }
      }
   }
}
/*******************************************/