Answer
At least $25$ throws.
Work Step by Step
The chance of us rolling two sixes at least once is one minus the probability of us not throwing two sixes, which is $1-(\frac{35}{36})^n$ after $n$ throws. This is because each throw is independent, and out of the $36$ possibilities $35$ are not two sixes. Hence $1-(\frac{35}{36})^n\geq0.5\\(\frac{35}{36})^n\leq0.5\\n\geq\log_{\frac{35}{36}}0.5\approx24.6$
Thus we need at least $25$ throws.
