Given,
Bandwidth(B)=64 kbps=64 x $10^3$ bps
$Tp = 270msec$
Length of packet (L)=$512 Byte= 512 \ast 8 bits $
$\therefore Tt= L/B=512 \ast 8/64 \ast 10^3 = 64 msec$
For maximum utilization window size should be,
$Ws= 1+2a$
$= 1+ 2 Tp/Tt$
$= 1+ 2 * 270/64$
$ = 1+ 8.44 $
$=9.44 \cong 10$