first off, let's convert the mixed fraction to "improper fraction" and then do the division.
[tex]\bf \stackrel{mixed}{6\frac{1}{2}}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}}\\\\
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\cfrac{6\frac{1}{2}}{\frac{1}{4}}\implies \cfrac{\quad \frac{13}{2}\quad }{\frac{1}{4}}\implies \cfrac{13}{2}\cdot \cfrac{4}{1}\implies \cfrac{13\cdot 4}{2\cdot 1}\implies \cfrac{52}{2}\implies \cfrac{26}{1}\implies 26[/tex]
