A washer man presents with thickness erosion & discoloration of web spaces of toes diagnosis is –
This washer man has fungal infection (thickening & erosion) of web space. Which may be either T pedis or candidal intertrigo. But, the examinar has not mentioned about specific lesions which :-


Red (erythematous) scaly lesion with central clearing and peripheral spreading → In T. pedis.
Red (erythematous) plaque with satellite pustules (peripheral pustules), and fine scales at periphery or some times white coloured plaque In candidal intertirigo.


T. pedis is not given in the option, so we are left only with candida.
T. unguium is the dermatophitic infection of nail (not web space)
Psoriasis
Tinea Unguium
Both
Candidiasis