html:

<input name="product" type="radio" value="Tarpaulins ">Tarpaulins
<input name="product" type="radio" value="stickers"> Vinyl Stickers<br>
<input name="product" type="radio" value="PhotoCanvas"> Photo Canvas

code:

if($product== "Tarpaulins" ){
            echo  "Tarpaulin rate : {$row['Tarpaulin_rate']}";
        }else if($product== "stickers"){
            echo  "stickers rate : {$row['stickers_rate']}";
        }else if($product== "PhotoCanvas"){
            echo  "Photo Canvas rate : {$row['PhotoCanvas_rate']} ";
        }

Apparently there's nothing wrong. Which error are you receiving?
$product is defined like: $product = $_POST['product']; ?