How to create a table corresponding to enum in EF6 Code First?

Since EF doesn’t handle it automatically, yes, this is the recommend way.

I suggest some modifications in article that you provided.

Rename your enum

public enum FacultyEnum { Eng, Math, Eco }

Create a class that represent the table

public class Faculty
{
    private Faculty(FacultyEnum @enum)
    {
        Id = (int)@enum;
        Name = @enum.ToString();
        Description = @enum.GetEnumDescription();
    }

    protected Faculty() { } //For EF

    [Key, DatabaseGenerated(DatabaseGeneratedOption.None)]
    public int Id { get; set; }

    [Required, MaxLength(100)]
    public string Name { get; set; }

    [MaxLength(100)]
    public string Description { get; set; }

    public static implicit operator Faculty(FacultyEnum @enum) => new Faculty(@enum);

    public static implicit operator FacultyEnum(Faculty faculty) => (FacultyEnum)faculty.Id;
}

Your model reference the class

public class ExampleClass
{
    public virtual Faculty Faculty { get; set; }
}

Create a extension method to get description from enum and seed values

using System;
using System.ComponentModel;
using System.Data.Entity;
using System.Data.Entity.Migrations;
using System.Linq;

public static class Extensions
{
    public static string GetEnumDescription<TEnum>(this TEnum item)
        => item.GetType()
               .GetField(item.ToString())
               .GetCustomAttributes(typeof(DescriptionAttribute), false)
               .Cast<DescriptionAttribute>()
               .FirstOrDefault()?.Description ?? string.Empty;

    public static void SeedEnumValues<T, TEnum>(this IDbSet<T> dbSet, Func<TEnum, T> converter)
        where T : class => Enum.GetValues(typeof(TEnum))
                               .Cast<object>()
                               .Select(value => converter((TEnum)value))
                               .ToList()
                               .ForEach(instance => dbSet.AddOrUpdate(instance));
}

Add the seed in Configuration.cs

protected override void Seed(Temp.MyClass context)
{
    context.Facultys.SeedEnumValues<Faculty, FacultyEnum>(@enum => @enum);
    context.SaveChanges();
}

Add the enum table in your DbContext

public class MyClass : DbContext
{
    public DbSet<ExampleClass> Examples { get; set; }
    public DbSet<Faculty> Facultys { get; set; }
}

Use it

var example = new ExampleClass();
example.Faculty = FacultyEnum.Eng;

if (example.Faculty == FacultyEnum.Math)
{
    //code
}

To remember

If you don’t add virtual in Faculty property, you must use Include method from DbSet to do Eager Load

var exampleFromDb = dbContext.Examples.Include(x => x.Faculty).SingleOrDefault(e => e.Id == 1);
if (example.Faculty == FacultyEnum.Math)
{
    //code
}

If Faculty property is virtual, then just use it

var exampleFromDb = dbContext.Examples.Find(1);
if (example.Faculty == FacultyEnum.Math)
{
    //code
}