reciprocal can be done only to a proper or improper fraction and not to mixed fraction... you may have to convert those to proper or improper fraction for sure then get the reciprocal.
Reciprocal can be done by dividing 1 to the number if it's whole number
example
2 has a reciprocal of 1/2 || 3 is 1/3
or
flipping the fraction over
example
2/3 has a reciprocal of 3/2 || 3/4 is 4/3
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let's try the first one of your number.
In order to convert mixed fraction to improper fraction you have to multiply the denominator to the whole number and add the numerator.
like this:
6 and 3/4
4 * 6 = 24 + 3 = 27
the result will be the numerator of the improper fraction and just copy the denominator
it will be 27/4
flip over to get the reciprocal
4/27
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another one
8 and 5/6
6 * 8 = 48 + 5 = 53
copy denominator
53/6
flip over
6/53
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last one
9 and 5/8
8 * 9 = 72 + 5 = 77
copy denominator
77/8
flip over
8/77
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you can reduce it to lowest term if possible
I hope this helps.