In any physics problem it's a good idea to start by defining exactly what we know and what we can infer.
What do we know? We know that the shingles fall 8.52 meters to the ground. So they go through a downward displacement, Δx, of 8.52 m.
What can we infer? We can infer that the shingles started falling from rest, so their original velocity, vo, was 0 m/s. We can also infer that they fell under the influence of normal Earth gravity, so their downward acceleration, a, was 9.81 m/s² (if we ignore air resistance). So we have three pieces of information:
Δx = 8.52 m
vo = 0 m/s
a = 9.81 m/s²
And we wish to know how much time, t, is required for the shingles to reach the ground.
t = ?
Now we need an equation that incorporates Δx, vo, a, and t (and nothing else). Fortunately, such an equation exists:
Δx = vo*t + 1/2at²
Because vo = 0 m/s, the term vo*t is also equal to zero and can be deleted from the formula:
Δx = 1/2at²
(8.52 m) = 1/2(9.81 m/s²)t²
(8.52 m) = (4.91 m/s²)t²
1.74 s² = t²
t = 1.32 seconds
I hope that helps. Good luck!