Let
x -----> Lisa's amount
y -----> Felipe's amount
z -----> Justin's amount
we have that
x+y+z=120 --------> equation A
x=z+6 ------> equation B
y=4z -----> equation C
substitute equation B and equation C in equation A
so
(z+6)+4z+z=120
solve for z
6z+6=120
6z=120-6
6z=114
z=$19
Find the value of x
substitute the value of z in equation B
so
x=19+6
x=$25
Find the value of y
substitute the value of z in equation C
y=4(19)
y=$76
therefore
Lisa's amount is $25
Felipe's amount is $76
Justin's amount is $19