Think of the simplest check you can make for a region.

# This does not work for the sample :D

def solve(data: str):
    # split input
    blocks = data.split("\n\n")
    shape_blocks = blocks[:-1]
    region_block = blocks[-1]

    # for every shape, get the number of occupied cells
    shape_area = []
    for shape_block in shape_blocks:
        shape_area.append(shape_block.count('#'))

    fit_regions = 0

    # for every region, check if the area is sufficient to fit all shapes
    for region_data in region_block.splitlines():
        size_data, shape_data = region_data.split(': ')

        # get region size
        m, n = [int(dim) for dim in size_data.split('x')]

        # get area needed to fit all shapes, without considering arrangement
        area_needed = 0
        for id, freq in enumerate(map(int, shape_data.split(' '))):
            area_needed += shape_area[id] * freq
        
        # if the region area is sufficient, count it as a fit (!!!)
        if m * n > area_needed:
            fit_regions += 1
    
    return fit_regions