I think they are going to fry in afternoon sun! And in any sun at all you will have to make sure they get enough water. They don't like their feet to be wet and to sit in soggy soil, but they will have to be watered fairly often, sun or no sun.
Linda C

Your begonias would do much better on the other side of the house where they would get just a little morning sun. The afternoon sun is going to be tough. Their preferred location is bright light but NO direct sun.

Watering...begonias can be a little tricky in pots. The soil needs to be just barely moist. But, even a little too much & they can rot. Within reason, best a day dry than a day too wet. They require excellent drainage. I'm assuming that your begonias are already potted & you're just going to hang them up "as-is"...? But, if you're going to be doing the potting...place some packing peanuts in the bottom of your pots to aid drainage.

Frankly, since I know large begonia baskets are expensive...I'd put them in another location & purchase something more suitable for your western exposure. If you bought them from a reputable nursery, I'm fairly certain they will take them back with the receipt or, at the least, exchange them.