Counter in two regimes: day and night

In this project we are given the AVR-STK500 board and a DSP which is supposed to send a waveform to the avr. The avr at its turn should recieve this signal, count its positive pulses and then display it. However, this is not the end. Now the avr should count these pulses in two separate regimes, one during the day and the other during the night and we need to multiplex them so that both counters use the same lcd, the Varitronix VI-402-DP. For what concerns the lcd, we are not allowed to use functions such as lcd.init(), but instead use 4 registers that store each digit and then display them. I will attach a scheme that may help make it clearer. If any of you have any resource that I could read so that I understand better, because even though I know what it needs to do conceptually, I feel a bit overwhelmed. Thank you very much, and I hope you have a great day!