Megasporogenesis and embryo sac

The megaspore mother cell (2n) undergoes meiosis to form four haploid megaspores, one of which develops into the embryo sac (female gametophyte).
All the cells of the embryo sac are formed by mitosis of the haploid functional megaspore, so the egg cell, the synergids and the antipodal cells are all haploid (n).
So the egg cell and the antipodal cells both have the haploid number of chromosomes.
The nucellus is the diploid (2n) tissue of the ovule, belonging to the parent sporophyte.
The megaspore mother cell is diploid (2n).
The secondary nucleus is formed by the fusion of the two haploid polar nuclei, so it is diploid (2n).
Every other pair contains at least one diploid structure, so the correct pair is egg cell and antipodal cells.

An embryo sac with 8 nuclei (7 cells) can develop in different ways:
Monosporic (Polygonum type, most common): from one functional megaspore after three mitotic divisions.
Bisporic (Allium type): from two megaspore nuclei.
Tetrasporic (e.g. Adoxa, Fritillaria): from all four megaspore nuclei.
In each of these types, the mature embryo sac can be 8-nucleate.
So an eight-nucleated embryo sac can be any of the above.