Answer
True.
$\displaystyle \sum_{j=1}^{6}2^j=\displaystyle \sum_{j=3}^{8}2^{j-2}$
Work Step by Step
$\displaystyle \sum_{j=1}^{6}2^j=2^1+2^2+2^3+2^4+2^5+2^6=2^{3-2}+2^{4-2}+2^{5-2}+2^{6-2}+2^{7-2}+2^{8-2}=\displaystyle \sum_{j=3}^{8}2^{j-2}$