Answer
$1.6\times 10^5$gallons
Work Step by Step
We know that
$E=\frac{m_U}{M_U}E_U$
$\implies E=\frac{1.0lb}{235u}(\frac{1Kg}{2.3lb})(\frac{1u}{1.66\times 10^{-27}Kg})(173\times 10^6eV)$
$E=2.05\times 10^{23}eV(1.60\times 10^{-19}J/eV)=3.2\times 10^{13}J$
Now we can find the required number of gallons of gas
$N=\frac{E}{E_{gasoline}}$
We plug in the known values to obtain:
$N=\frac{3.2\times 10^3}{2.0\times 10^8}$
$N=1.6\times 10^5$gallons