Se requiere asesoramiento sobre consultas de MySQL

Así que empieza con eso:

SELECT * 
FROM shop_product_properties
WHERE name = 'Insert Style';

Luego introduzca una subconsulta:

SELECT * 
FROM shop_product_properties
WHERE name = 'Insert Style'
AND product_id IN (
    SELECT DISTINCT product_id
    FROM shop_product_properties
    WHERE name = 'First Choice Material'
    AND value = 'Gold'
);

http://sqlfiddle.com/#!2/ecfb4/1