Use int.Parse or int.TryParse rather than Convert.ToInt32. Confirm you are entering a valid string. Split the code into different lines so you can tell exactly where the error is:
int productQuantity = int.Parse(newProduct_Quantity.Text);
sqlInsert.Parameters.Add("Product_Quantity", SqlDbType.Int).Value = productQuantity;
Also note that you don't need the "@" in front of the variable... that will be added for you. If you are calling a stored procedure, make sure the parameter is the right type. If you are using an INSERT statement, make sure all the parameters and values are in an order that corresponds to eachother.