Let the leaves be $a,b,c,d,e,f,g,h$
Path length $0:a-a,b-b,c-c....h-h=8$
Path length $2: a-b,b-a,c-d,d-c,e-f,f-e,g-h,h-g=8$
Path length $4:a-\fbox{n}-\fbox{n}-\fbox{n}-c$
$\underbrace{a-\fbox{n}-\fbox{n}-\fbox{n}-d}$
a is having 2 choices after
reaching two levels up
Similarly $'b'$ is having 2 choices
Similarly $'c'$ is having 2 choices: $c-\fbox{n}-\fbox{n}-\fbox{n}-a$
$\underbrace{c-\fbox{n}-\fbox{n}-\fbox{n}-b}$
.
.
$\therefore 8$ leaves each having $2$ choices $8\times 2=16$
Path length $6:$ $a-\fbox{n}-\fbox{n}-\fbox{n}-\fbox{n}-\fbox{n}-e$
${a-\fbox{n}-\fbox{n}-\fbox{n}-\fbox{n}-\fbox{n}-f}$
${a-\fbox{n}-\fbox{n}-\fbox{n}-\fbox{n}-\fbox{n}-g}$
$\underbrace{a-\fbox{n}-\fbox{n}-\fbox{n}-\fbox{n}-\fbox{n}-h}$
a is having 4 choices after
reaching root
Similarly $'b'$ is having 4 choices
Similarly $'c'$ is having 4 choices
.
.
$\therefore 8$ leaves each having $4$ choices $8\times 4=32$