The answer is:Â Â "Â
 " .Â
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Explanation:
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Given the fractions:Â
"3/4" ; Â and "1/8" ;Â
Note the "denominators: Â "4" and "8" .
We can easily convert "3/4" to its fraction value with a denominator of "8" ;Â
→ "3/4" =  " (what value?) / 8"  ?
→  Look at the "denominators" :
Â
 →  4 * (what value?) = "8" ? ;  → "8 ÷ 4 = "2" ;Â
→ So, 4 * 2  = 8 ;  for the "denominator" ;  so we multiply by "2" in theÂ
"numerator" , as well:
→ "(3/4)" = (3*2)/(4*2) = "6/8" ;
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→  "3/4"  =  "6/8" ;Â
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→  Note:  The entire batch of cookies is:  "8/8" ; or "1 whole" ;Â
    {since:  "8/8" = "{8÷8 = 1 whole}" ;Â
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Given: Â "3/4" of the {entire batch of} his cookies are chocolate chip." ;Â
i.e. Â Â "6/8 out of 8/8" are chocolate chips ; Â
Â
6/8 are chocolate chips;
1/8 out of 6/8 are {"chocolate chip with nuts"} ;
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 ==> What fraction of cookies are {"chocolate chip with nuts"} ?
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To get the answer; Â we simplify: Â "1/8 out of 6/8"; Â
or, simplify, "1/8 out of 3/4" ;Â
that is:
"Â
 ÷ Â
" = ? {our answer} ?? ;Â
→  "Â
 ÷ Â
" ;
→  Note:  When we divide 2 (TWO)  fractions;  we find the equivalent by writing the expression with a multiplication sign; AND by "inverting" (or taking the "reciprocal" of) the "second" fraction ;Â
  =    "Â
 * Â
" ;Â
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Note: Â The "4" cancels out to a "1" ; and the "8" cancels out to a "2" ;Â
since:  "{8 ÷ 4 = 2}" ;  and since:  "{4 ÷ 4 = 1 }" ,
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And we can rewrite the expression as:
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 Â
→   "Â
 * Â
" ;Â
And simplify further:
   =  "Â
 ;Â
   =  "Â
" .
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The answer is: Â "Â
" .
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 Variant:  At the point {above} which we have:
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 →    "Â
 * Â
" ;Â
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Simplify further; as following:Â
    =  "
;Â
    =  "
" ;
    =  " (4 ÷ 4) / (24 ÷ 4) "  ;
Â
    =  "
" .
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The answer is: Â "Â
" .Â
_______________________________________________________Â