Question 773185
Suggestion, convert EVERYTHING to gallons first, and then setup your proportion.


1/4 cup for the mixing solution is 1/4 of 8 fluid ounces, and this is 2 fluid ounces.  1 gallon contains 128 fluid ounces.  
{{{2*(1/128)}}} {{{(fluidOz*gal/fluidOz)}}}
{{{1/64}}} gallons


The 1 pint of water to make the current desired mixture is {{{1/8}}} gallon, since 1 pint is {{{1/8}}} gallon.


Ready to make the proportion.  Let's try to put the "mixing solution" in the numerator position for one of the ratios.  v = volume of mixing solution in gallons.


Direction Ratio:  {{{(1/64)/1}}}

Our Mixture Ratio:  {{{v/(1/8)}}}

Our Proportion:  {{{highlight(v/(1/8)=(1/64)/1)}}} _________Remember, gallons was chosen for units.  v is in gallons and you may need to convert to other units, like maybe cups or pints or fluid ounces.
SOLVE FOR v.


SIMPLIFYING THE PROPORTION AND SOLVING

{{{v*8=1/64}}}
{{{v=1/(8*64)}}}
{{{highlight(v=1/512)}}}  which is one-eighth of a quarter of a cup.  Very small.  Choosing fluid ounces would be more practical.  


A choice of fluid ounces to begin the whole problem solving may be easier than the choice of gallons.  


ANOTHER WAY:

If you can see the proportion in your head, then maybe you can start choosing quantities and units earlier than written analysis.  Basic recipe says, 1 gallon of water, but your mixture uses 1 pint = 1/8 gallon of water.  This means your mixture will be 1/8 of the basic recipe.  Now, what is 1/8 of the 1/4 cup?  This would be {{{(1/8)(1/4)=highlight(1/32)}}} cup.
With that, you can use the fact, 1 cup = 8 fluid ounces, and then ----
{{{(1/32)(8/1)}}} {{{cup*(fluidOz/cup)}}}
{{{highlight(1/4)}}} fluid ounce