We can create a system of equations with the information we know.
J = 4L
J + L - 6 = 64
The first equation is pretty self-explanatory. Jack is 4 times as old as Lucy. The second equation is just adding their ages together. We subtract 6 because the sum of their ages was 64 three years ago. Three years ago, both Jack and Lucy were 3 years younger (total of 6).
Substitute 4L in for J in the second equation and solve.
4L + L - 6 = 64
5L = 70
L = 14
If Lucy is 14, then Jack is 14*4 = 56.