Understanding 2's complement multiplication using Booth's algorithm
So, it goes like this, we have Q = 0011 and Q-1 = 0 in the beginning.
At the start, we have

count = 4(Q0 Q-1) = (1 0)

so we perform the A←(A-M) operation, according to the figure each time when we perform any operation in register A, we assume that its value is 00000000 for +M and 11111111 for −M. Performing A←(A-M) yields the first partial product

A = 11111111+00001001 = 11111001

Now, we have

count = 3(Q0 Q−1) = (1 1)

note here, when we have (Q0 Q−1) as (1 1) or (0 0), we'll just skip and put all 0s in the partial product by shifting it by 1 bit to the left (as we do in multiplication) as it's done in the book, which is the 2nd partial product

A = 00000000+00000000 = 00000000shifting it left by 1 bit, 00000000

Now, we have

count = 2(Q0 Q−1) = (0 1)

so we perform the (A←A+M) operation, which gives us the 3rd partial product

A = 00000000+00000111 = 00000111shifting it left by 2 bits, 00011100

Now, we have

count = 1(Q0 Q−1) = (0 0)

as mentioned above, we'll just skip and put all 0s as the 4th partial product

A = 00000000+00000000 = 00000000shifting it left by 3 bits, 00000000(this isn't illustrated in the figure 9.14(a))

after this operation count = 0 and then we'll sum up all the partial products as
   11111001 (1st partial product)
   00000000 (2nd partial product)
   00011100 (3rd partial product)
 + 00000000 (4th partial product)
-------------------
   00010101 (final product)

As we all know (00010101)2 = (21)10. That's what done in the figure 9.14(a), but shown in a different (or COMPACT) way as
   11111001
   0000000
 + 000111
-------------------
   00010101

Well, you can make it more compact like this:-
   11111001
 + 000111
-------------------
   00010101

But all of 'em will give you the binary representation of 21.