Answer
$$a^{3}$$
Work Step by Step
To multiply powers of the same base, add the exponents:
$$\frac{(2a^{4})(3a^{2})}{6a^{3}}=\frac{2\times a^{4}\times 3\times a^{2}}{6a^{3}}=\frac{2\times 3\times a^{4+2}}{6a^{3}}=\frac{6a^{6}}{6a^{3}}.$$
To divide powers of the same base, subtract the exponents:
$$a^{6-3}=a^{3}.$$
