The product \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}=\mathrm{CHCOCH}_{3}\) is obtained by the mixed aldol reaction of (a) benzaldehyde and acetone (b) acetophenone and acetone (c) cyclohexanone and propanal (d) benzaldehyde and acetaldehyde

The product of the mixed aldol reaction is given as C6H5CH=CHCOCH3. In aldol reactions, the product is characterized by the presence of a new carbon-carbon bond (C-C bond) next to the carbonyl group (\(CO\)). Thus, we can break down the product to help identify the reactants. Phenyl group \(C_{6}H_{5}\) represents a benzene ring and the rest of the product is \(CH=CHCOCH_{3}\).

Let's analyze each of the options to determine which reactants will produce the given product in a mixed aldol reaction. (a) benzaldehyde and acetone - Benzaldehyde has a structure of \(C_6H_5COH\) and acetone has a structure of \(CH_3COCH_3\). While both compounds have carbonyl groups, benzaldehyde doesn't have any alpha hydrogens, and therefore a base won't be able to create an enolate ion. Hence, this option is not suitable for the aldol reaction. (b) acetophenone and acetone - Acetophenone has a structure of \(C_6H_5COCH_3\) while acetone remains \(CH_3COCH_3\). In this case, both molecules feature a carbonyl group, and acetophenone has an alpha hydrogen that can participate in an aldol reaction with acetone. (c) cyclohexanone and propanal - Cyclohexanone has a structure of \(C_6H_{10}O\) and propanal has a structure of \(CH_3CH_2CHO\). These two carbonyl compounds could participate in an aldol reaction, but the product structure does not match the required structure for the given product. (d) benzaldehyde and acetaldehyde - Benzaldehyde has a structure of \(C_6H_5COH\) and acetaldehyde has a structure of \(CH_3CHO\). As mentioned earlier, benzaldehyde does not have an alpha hydrogen, so it is not suitable for the aldol reaction.

After analyzing each option and their potential to produce the given product, we identify that option (b) acetophenone and acetone will yield the product C6H5CH=CHCOCH3 through the mixed aldol reaction. The other options either lack the necessary alpha hydrogens for the reaction or don't lead to the formation of the correct product structure.