I strongly recommend you to use Eloquent, instead of pure SQL. It's one of the most beautful things in Laravel. Two models and relations and it's done! If you need to use pure SQL like that, put it all in DB::raw
. It's easier, simpler and (ironically) less messy!
With the models, you could use relations between the two tables (represented by the models itself) and say (so far I understood) that Brands belongs to Products, and Images belongs to Product. Take a look at Eloquent's documentation on Laravel. Probably will be more clearly.
Once the relations are done, you can only say that you wanna get
$product = Product::where(function ($query) use ($brand){
$brand_id = Brand::where('brand', '=', $brand)->first()->id;
$query->where('brand_id', '=', $brand_id);
})
->image()
->get();
That and a better look at Eloquent's documentation should help you to do the job.
P.S.: I didn't test the code before send it and wrote it by head, but i think it works.