Step 1: Recall the rule.
An alkene shows geometrical isomerism only if each carbon of the double bond carries two different groups. If a carbon has two identical groups, it cannot show this isomerism.
Step 2: Test compound I.
Compound I is $(CH_3)_2C=CH\,C_2H_5$. One double-bond carbon has two identical methyl groups, so it has no geometrical isomerism.
Step 3: Test compound II.
Compound II is $C_6H_5CH=CH\,C_2H_5$. One carbon has H and phenyl, the other has H and ethyl. Both carbons carry different groups, so it shows geometrical isomerism.
Step 4: Test compound III.
Compound III is $C_6H_5CH=CH_2$. The end carbon has two identical hydrogens, so it has no geometrical isomerism.
Step 5: Test compound IV.
Compound IV is $CH_3CH=C(Cl)CH_3$. One carbon has H and methyl, the other has Cl and methyl. Both carry different groups, so it shows geometrical isomerism.
Step 6: Pick the answer.
Only compounds II and IV satisfy the rule. \[ \boxed{\text{II and IV only}} \]