Given logical address = 48 bits and the addressing is byte addresable type..
So logical address space = 248 B
Given page size = 16 kB = 214 B
So no of pages = 248-14 = 234
So no of entries in page table = 234
Also no of frames = 16 GB / 16 kB = 220
So no of frame bits = log2 220 = 20 bits
So no of bits in 1 page table entry = 20 + 2(for protection as mentioned in question)
= 22 bits
So page table size = 234 * 22
= 22 * 16 Gb
= 22 * 2 GB
= 44 GB
Hence size of page table = 44 GB