Cepheid variables have been found in the SBcII galaxy NGC 4496A, parent to the Type Ia supernova 1960F. Of the 130 variables discovered with the Hubble Space Telescope (HST) over a 70 day observing internal from 1994 June to August, comprising 17 epochs in the F555W band and four epochs in the F814W band, 95 are bona fide Cepheids. The periods range from 7 days to greater than 70 days, with the mean magnitudes ranging from <V> = 24.4 to 26.8. The distance modulus of NGC 4496A, based on the Cepheids, is (rn-Al)0 = 31.03±0.14, where a formal reddening of E(V-I) = 0.04±0.06 derived from the colors of the Cepheids has been used to account for possible extinction. There is no measurable differential reddening over the field. The absolute magnitudes of SN 1960F at maximum are M(B)max = -19.43±0.17 and M(V)max =-19.52±0.21. Combining these absolute magnitudes with the Hubble diagrams of "Branch normal" Type Ia supernovae (SNe Ia), determined earlier, gives Hubble constants, based on SN 1960F alone, ofHO(B)=56±9 km s-1, (1) and H0(V) = 55±9 km s-1. (2) Combining the calibration of SN 1960F here with six other extant calibrations set out in Paper VII gives interim mean absolute magnitude calibrations of M(B) = -19.45±0.07 and 4M(V) max = -19.47±0.07, with no evidence for appreciable dependence on the light-curve decay rate. These mean interim calibrations require H0(B) = 57±4 km s-1 and H0(V) = 58±4 km s-1 Mpc-1.