Aims: We present spatially resolved high-resolution spectrophotometric data for the planetary nebulae PB 8, NGC 2867, and PB 6. We have analyzed two knots in NGC 2867 and PB 6 and one in PB 8. The three nebulae are ionized by [WC] type nuclei: early [WO] for PB 6 and NGC 2867 and [WC 5-6] in the case of PB 8. Our aim is to study the behavior of the abundance discrepancy problem (ADF) in this type of planetary nebula. Methods: We measured a large number of optical recombination (ORL) and collisionally excited lines (CEL), from different ionization stages (many more than in any previous work), thus, we were able to derive physical conditions from many different diagnostic procedures. We determined ionic abundances from the available collisionally excited and recombination lines. Based on both sets of ionic abundances, we derived total chemical abundances in the nebulae using suitable ionization correction factors. Results: From CELs, we have found abundances typical of Galactic disk planetary nebulae. Moderate ADF(O++) were found for PB 8 (2.57) and NGC 2867 (1.63). For NGC 2867, abundances from ORLs are higher but still consistent with Galactic disk planetary nebulae. On the contrary, PB 8 presents a very high O/H ratio from ORLs. A high C/O was obtained from ORLs for NGC 2867; this ratio is similar to C/O obtained from CELs and with the chemical composition of the wind of the central star, indicating that there was no further C-enrichment in the star, relative to O, after the nebular material ejection. On the contrary, we found C/O<1 in PB 8. Interestingly, we obtain (C/O)ORLs/(C/O)CELs < 1 in PB 8 and NGC 2867; this added to the similarity between the heliocentric velocities measured in [O iii] and O ii lines for our three objects argue against the presence of H-deficient metal-rich knots coming from a late thermal pulse event. Based on data obtained at Las Campanas Observatory, Carnegie Institution. Table 3 is only available in electronic form at http://www.aanda.org