Step 1: Understand the effect of water table depth on bearing capacity.
The bearing capacity of a footing is influenced by the position of the water table relative to the base of the footing. If the water table lies at a depth equal to or greater than the width of the footing (\( B \)), its effect on bearing capacity is minimal. Given: Footing size = $ 3 \, \text{m} \times 3 \, \text{m} $
Minimum required depth of water table = $ B = 3 \, \text{m} $
Step 2: Analyze each option.
$ 6 \, \text{m} $: Water table is deep enough; no effect on bearing capacity.
$ 2 \, \text{m} $: Water table is too shallow; affects bearing capacity.
$ 3 \, \text{m} $: Just at the minimum safe depth; no significant effect.
$ 4.5 \, \text{m} $: Also safe but deeper than necessary.
Step 3: Select the correct option.
The minimum depth of water table below the footing base to avoid affecting bearing capacity is: $$ \boxed{3 \, \text{m}} $$