what i am getting is :
Total No. of Pages= 252
Page Size= 212 Bytes and Entry size from part (a) 8 Bytes (64 Bits).
No. of Entries=Page Size/Entry Size=212-3=29
So Page Table Size=252 * 8 Bytes = 255 Bytes
Here we cannot fit Page Table into Single Page (255 --> 212)
So No. of Pages Required to fit a Page Table = 255/212 = 243 Pages
Here as per Question Each Page Table fits into Single Page so we would required 243 Page Tables to Store 255 Bytes.
Now No. of Levels in Paging:
Last Level : Total Page Table =243
Second Last Level : Total Page Table =243/29 = 234
Third Last Level : Total Page Table =234/29 = 225
Fourth Last Level : Total Page Table =225/29 = 216
Fifth Level : Total Page Table =216/29 = 27
So Total No. of Levels=6