Final answer:
The order on Shabbat Chanukah starts with lighting the Shabbat candles, followed by Shabbat blessings, and then the Chanukah menorah is lit, accompanied by Chanukah blessings.
Step-by-step explanation:
The order of lighting and blessings on Shabbat Chanukah begins with the Shabbat candles, which are lit first. Following the customary practice of welcoming Shabbat, the blessings over the Shabbat candles are recited. Subsequently, the Chanukah menorah is lit. This involves lighting the candles from left to right, with the newest candle lit first; but the actual order of the blessings reverses, beginning with the blessings specific to Chanukah and ending with the Shehechiyanu blessing if it is the first night of Chanukah. It is unique in combining the traditions of two holidays, intertwining the sanctity of Shabbat with the historical commemoration of the miracle of the oil in the Chanukah story.