To find the reciprocal of a fraction, you simply swap the numerator and the denominator.
Given the fraction [tex]\(\frac{3}{6}\)[/tex], the reciprocal would be [tex]\(\frac{6}{3}\)[/tex].
Thus, the expression [tex]\(4 \div \frac{3}{6}\)[/tex] can be rewritten as:
[tex]\[
4 \times \frac{6}{3}
\][/tex]
So the reciprocal of [tex]\(\frac{3}{6}\)[/tex] is [tex]\(\frac{6}{3}\)[/tex].