The probability of a normally distributed random variable being within 7.7 standard deviations is practically 100%.
Remember these rules: 68.2% of the probability density is within one standard deviation; 95.5% within two deviations, and 99.7 within three deviations.
The reason that tables don't go to 7.7 is because deviations beyond around three are of little practical use. If you see a random variable being out by 7.7 deviations, this is so unlikely that you should suspect something is wrong with the experiment.
To calculate the exact answer, you have to simply figure out the area under the bell curve between 0 and 7.7 and then multiply by two. To do that, you need the cumulative density function: i.e., the integral of the probability density function. Unfortunately, that function does not exist in closed form.
Since you're expected to compute this for homework, your teacher must have given you some tools by which he or she expects you to calculate cumulative densities that are not covered by your table.
Here is a paper about approximating the cumulative density function.
Scientific calculators which provide support for statistical computing often have a function for this. You enter an argument like 7.7, and the function computes the cumulative density from $-\infty$ to the argument: i.e. the area under the curve to the left of the argument. If you have such a function, then simply get the value for 7.7, and then subtract from that the value for -7.7.
Your calculator most likely performs this calculation using numerical integration over the probability density function, rather than an approximation formula.