Keg, 28 bytes (SBCS)

0&{:1>|:2%[3*9|1⁄2]&9&}_&

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Explanation

0& # Set 0 to the accumulator
 {:1> # While the number is not 1:
 |:2% # Is the number divisible by 2?
 [3*9 # If not, multiply by 3 & increment
 |1⁄2] # Otherwise, halve the number
 &9& # Increment the accumulator
 }_ # Discard the number
 & # Push the accumulator & implicit output

Keg -rR, 23 bytes (SBCS)

^{I really need to remember those new instructions.}

0&{:1>|:2%[3*9|1⁄2](6)

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