let's say the 3 pieces are a, b and c.
a = shortest piece
b = middle piece
c = longest piece
we know that a + b + c = 56, that's the length of the sandwich, rather long, but heck.
since the shortest piece is a, and the middle piece is 6 longer than that, then b = a + 6.
we also know the shortest piece is 8 less than the longest, well, c is the longest, and 8 less than that is c - 8, thus a = c - 8, and therefore a + 8 = c.
[tex] \bf \stackrel{a}{a}~~+~~\stackrel{b}{(a+6)}~~+~~\stackrel{c}{(a+8)}~~=~~56\implies 3a+14=56\implies 3a=42
\\\\\\
a=\cfrac{42}{3}\implies \boxed{a=14}
\\\\[-0.35em]
~\dotfill\\\\
b=(14)+6\implies \boxed{b=20}~\hspace{7em}c=(14)+8\implies \boxed{c=22}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
~\hspace{11em}14+20+22=56 [/tex]
