Since this is an assignment, I'll move this thread to the fitting homework forum. Please be aware that we will not do your homework or assignment. Rather we will guide you through the process so you can arrive at your own solution.
Believe me, this is a well practiced procedure and you will gain much more understanding this way.
Meanwhile here are a few tips to get you started:
Operating conditions will be mainly dictated by the LEDs you use. So your first decision has to be on the type of LEDs. Different LEDs have different requirements in terms of voltage and current.
Once you have settled on a specific LED type, you can determine the topology, i.e. series or parallel connection or a mixture of both serial and parallel connection of the LEDs to optimize pow utilization.
Check the parameters of the "9 V " panel. What is the real output voltage under load and under normal daylight lighting conditions (cloudy day). Depending on the outcome a suitable battery can be chosen.
Note that NiMh, the battery tape of choice in your team, charges to approx.1.4 V when full and discharges to approx. 1.2 V when empty. The number of cells to use in series depends on the max. voltage of the cells and the min. voltage of the solar panel.
You will then need
- a charging circuit to charge the battery. A linear circuit can only charge to battery voltages lower than the panel's voltage. A switch mode charger can charge to higher voltages, too (boost charger).
- a driver circuit to drive the LEDs (see our resource). Possibly a simple series resistor can be used in your project.
As for the required battery capacity: From the LED circuit (parallel, serial, see above) you can determine current required. Current times on-time gives the required min. capacity in milliamperehours (mAh). Taking into consideration that batteries cannot be drained from 100% charge state to 0 % charge state, only approx.80% of the battery capacity are useable. Add some loss due to aging and use e.g. 50% as long-time useable capacity. From the required load current and time (above value in mAh) get the battery capacity by dividing by these 50% (or simply multiply by 2).
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