The DH114 was enroute Undara-Weipa, cruising at 10,000 ft and estimating abeam Cohen at 1505. The C402, Aurukun-Cairns was estimating Holroyd River at 1505, had planned at 9,000 ft but, approaching that level, the pilot advised climbing to 10,000 ft and requested traffic. The flight service operator mentally projected the track of the DH114 on the chart (the Aurukun-Cairns track had already been marked on the chart) and assessed that, based on the respective abeam Cohen and Holroyd River estimates, there would be no traffic confliction. Shortly after reporting abeam Cohen, the pilot of the DH114 advised that another aircraft had passed close by, in the opposite direction, and at the same level. This aircraft was later identified as the C402. The flight service operator was working area 7 and area 5 combined. The level of activity in these areas had become very busy, but not unmanageably so, in the period leading up to the occurrence. The operator said, that when the pilot of the C402 requested traffic and he had assessed there would be no confliction, the track he had mentally plotted had been incorrect. One reason for this was that the track crossed two charts which were displayed at separate parts of his console. Another was that the position of Undara used by the operator was incorrect. The operator said that he had intended to plot the Undara-Weipa track on the chart to confirm his mental calculation but had forgotten to do this in the time available.