In the given molecule Pyrene , the π bond shown in green is in cross conjugation (shown in green in figure 1). This bond( figure 2) is excluded from interaction with rest of conjugated system. Hence , the central $\ce{C=C}$ isn't hosted by the largest p orbital loop, so it's not counted towards Hückel's rule for aromaticity.
The outer periphery (shown in blue in figure 3), is a loop of $\ce{14 π}$ electrons , therefore aromatic. This may be possible hückel double bond you are referring to.
The π bond in cross-conjugation (shown in green) maybe non-hückel double bond.
