The relatively young, high-excitation planetary nebula (PN) NGC 6886 shows a remarkable variety of lines from both high- and low-excitation stages, i.e., from N0 to N4+, and as a result it provides unique opportunities for detailed studies of physical processes, using a theoretical model. By combining Hamilton echelle observations with UV data secured with the International Ultraviolet Explorer (IUE) satellite, and with available IR data, we can obtain improved diagnostics and elemental abundances which should supply insights into nucleogenesis processes and properties of the progenitor star. Improved theoretical nebular models are employed. The chemical composition of this high-excitation PN is found from ionic concentrations, and also from a theoretical model. Except for Ne, Si and cl, the agreement between the abundances calculated using the two methods is generally remarkably good. The C/H ratio is enhanced by about 15-20 per cent above the solar value, but the N/H and Ne/H, and probably Si/H ratios, are close to those of the Sun. The other 'metal'/H ratios and the He/H ratio seem to be lower than in the Sun, and O is depleted. If pronounced T(epsilon) fluctuations are assumed, we can raise the abundances of O, S, Cl and Ar to approximately solar values, but then C, N and Ne are substantially enhanced. Since the distance is poorly determined, it is difficult to establish evolutionary parameters.