I think you should update your question with something you have tried. Even a piece of code you tried to accomplish your goal.When you need to fetch data and add those data into a drop down you can follow below steps.

1.Fetch data from DB.

2.Assign each of data into drop down options with a while loop

    <div class="form-group">
    <label class="col-md-2 control-label">Machine_vin numbers </label>
    <div class="col-md-4">
        <select  class="form-control"  name="machine_vin" required>
            <option  value="0" selected disabled>Select the type of Machine vin number</option>
            <?php
             //fetch data from db
            $sql_machine_vin = ' SELECT * FROM  repair';
             // query the sql with db connection           
            $result_machine_vin = mysqli_query($conn,$sql_machine_vin);
             //loop the result
            while($row_machine_vin =mysqli_fetch_array($result_machine_vin)){
            ?>

             <option  value="<?=$row_machine_vin['Machine_vin'];?>" >
             <?=$row_machine_vin['Machine_vin'];?> ></option>
             <?php
            }
            ?>
        </select>
    </div>>