If y varies inversely as x, and y=4b when x=6a, what is y in terms of a and b when x=8

if y varies inversely as x, xy = k
so k = 4b*6a = 24ab

8y = 24ab
y = 3ab
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1st way:
here , y=1/x
or, xy=1
or, 6a×4b=1
or, ab=1/24
again, xy=1
or,8y=1 [when, x=8]
or,y=1/8
or, y=3×(1/24)
or,y=3ab (showed)

another way,

here, y=1/x
or, xy=1
again, x=6a
or, 8=6a [when, x=8]
or,a=4/3 .......(1)
also, y=4b
or,y=3×(4/3)×b
or, y=3ab [from ,(1)]
then, y=3ab