First, we recommend using a SH68-68-EP cable to connect a PCI-6036E to a BNC-2111 (see the BNC-2111 Manual, Table 2, page 4 for more information on connections).
The PCI-6036E has two onboard counters, ctr0 and ctr1. You can use either of these counters to count the pulses from the encoder in either direction using the counter's source and gate pin. On the PCI-6036E, the ctr0 source is PFI 8, the ctr0 gate is PFI 9, the ctr1 source is PFI 3, and the ctr1 gate is PFI 4. However, none of these lines are directly accessible on the BNC-2111. The only PFI lines that are exposed on the BNC-2111 are PFI 0, 2, 7, 12, and 13. Therefore, you will need to use software to internally route the exposed PFI lines (0, 2, 7, 12, and 13) to the desired counter source and gate PFI lines (3 and 4 or 8 and 9). This should be possible on the PCI-6036E because there are indirect routes between those terminals.