Delta Cephei has a period of about P = 5.25 days,
and an average apparent V-band magnitide of about m(V) = 4.2.
To find the absolute magnitude, use
M(V) = -1 - 2.8*log10(period)
= -3.0
Now, use the distance modulus to calculate the distance
(m - M) = 4.2 - (-3.0) = 7.2
= 5*log10(d) - 5
12.2/5
--> d = 10
= 270 pc