| You need both pieces of information, but this info isn't complete.
First, you'd have to know how much was charged to Other Expense.
Second, the deal with the rent only says what was paid on what date. But in order to do an adjusting entry you would need to know how much of that was for the current year and how much goes into the future.
You cannot start trying to memorize all the adjusting entries, because there could be a lot of different ones. Some texts have just a small sampling and they do them alike each time. But some books present the information in different ways, and you'll need to understand what is behind them and how they are done in order to figure them out. Like the supply one is pretty weird. Some is in supplies where it belongs; some got charged to an expense. That's almost more like real life when things aren't done consistantly than like what most texts do.
Both of these entries are deferred expenses, meaning they are paid for up front and then expense later as they are used up. An entry for a deferred expense is normally to debit the expense for the used part and credit the asset. But the supplies was partly charged to an expense already, so that's a little different. In the end, you need to know how much existed in total, how much you still have, and therefore how much must have gotten used... and then make sure the Supplies Expense and Supplies accounts have the right balances in them. | 
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