Parsed program:
append([],Y,Y).
append([X|L],Y,[X|Z]) :- append(L,Y,Z).

Parsed query: 
append([1,2,3],[4,5,6],W).

Entering BC
Current goal: append([1,2,3],[4,5,6],W).
Additional goals: 0
Unified goal append([1,2,3],[4,5,6],W). and clause append([X2|L2],Y2,[X2|Z2]) :- append(L2,Y2,Z2).
Substitution:
    'X2'    '1'    
    'L2'    '2,3'  
    'Y2'    '4,5,6'
    'W'     'X2|Z2'


Entering BC
Current goal: append([2,3],[4,5,6],Z2).
Additional goals: 0
Unified goal append([2,3],[4,5,6],Z2). and clause append([X4|L4],Y4,[X4|Z4]) :- append(L4,Y4,Z4).
Substitution:
    'X4'    '2'    
    'L4'    '3'    
    'Y4'    '4,5,6'
    'Z2'    'X4|Z4'


Entering BC
Current goal: append([3],[4,5,6],Z4).
Additional goals: 0
Unified goal append([3],[4,5,6],Z4). and clause append([X6|L6],Y6,[X6|Z6]) :- append(L6,Y6,Z6).
Substitution:
    'X6'    '3'    
    'L6'         []
    'Y6'    '4,5,6'
    'Z4'    'X6|Z6'


Entering BC
Current goal: append([],[4,5,6],Z6).
Additional goals: 0
Unified goal append([],[4,5,6],Z6). and clause append([],Y7,Y7).
Substitution:
    'Y7'    '4,5,6'
    'Z6'    '4,5,6'


Entering BC
Found answer
    'X2'    '1'    
    'L2'    '2,3'  
    'Y2'    '4,5,6'
    'W'     'X2|Z2'
    'X4'    '2'    
    'L4'    '3'    
    'Y4'    '4,5,6'
    'Z2'    'X4|Z4'
    'X6'    '3'    
    'L6'         []
    'Y6'    '4,5,6'
    'Z4'    'X6|Z6'
    'Y7'    '4,5,6'
    'Z6'    '4,5,6'

Exiting BC
Exiting BC
Exiting BC
Exiting BC

Query: append([1,2,3],[4,5,6],W).
Yes

answer = 
    'W'        '1,2,3,4,5,6'