Total number of ways to choose 4 shoes = $\Large\binom{24}{4}$
The probability of at least 1 complete pair of shoes is chosen = 1 - Probability of no complete pair is chosen
The probability of at least 1 complete pair of shoes is chosen $=1-\frac{24*22*20*18}{24*23*22*21}$ or $1-\frac{\binom{12}{4}*2^4}{\binom{24}{4}}$$