First loop prints each letter of hospital on a line by incrementing the the counter per letter.  Strings start at position 0

#!/usr/bin/env python

place=”hospital”
length=len(place)
print(‘hospital has’,length,’letters’)
counter=0
print(”)

print(‘print each letter at a time’)
while place[counter:]:
print(place[counter])
counter+=1

hospital has 8 letters

print each letter at a time
h
o
s
p
i
t
a
l

This is created by a nested while loop.  Each loop starts at 0 and increments to the length of hospital.  When outside loop increments it seeds the number for the inside loop to begin with.   i must be less than j.   If i=j, it will print a blank line. 

print(‘slicing strings’)
i=0

while i <= length:
   j=i
  while j <= length:
      print(place[i:j])
      j+=1
   i+=1
   print(”);

slicing strings

h
ho
hos
hosp
hospi
hospit
hospita
hospital


o
os
osp
ospi
ospit
ospita
ospital


s
sp
spi
spit
spita
spital


p
pi
pit
pita
pital


i
it
ita
ital


t
ta
tal


a
al


l

I added if i not equal to j, to not print the blank.  I added the print(i, ‘   ‘j) to show you what prints at each increment.

i=0
while i <= length:
   j=i
   while j <= length:
      if i!=j:
         print(i,’ ‘,j)
         print(place[i:j])
      else:
        print(i,’ ‘,j)
        print(”)
    j+=1
   i+=1
   print(”);

0 0   #prints nothing

0 1
h
0 2
ho
0 3
hos
0 4
hosp
0 5
hospi
0 6
hospit
0 7
hospita
0 8
hospital

1 1   #prints nothing

1 2
o
1 3
os
1 4
osp
1 5
ospi
1 6
ospit
1 7
ospita
1 8
ospital

2 2 #prints nothing

2 3
s
2 4
sp
2 5
spi
2 6
spit
2 7
spita
2 8
spital

3 3   #prints nothing

3 4
p
3 5
pi
3 6
pit
3 7
pita
3 8
pital

4 4  #prints nothing

4 5
i
4 6
it
4 7
ita
4 8
ital

5 5   #prints nothing

5 6
t
5 7
ta
5 8
tal

6 6  #prints nothing

6 7
a
6 8
al

7 7   #prints nothing

7 8
l

8 8   #prints nothing

Process finished with exit code 0