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Let's go over how a carbocation can form from an alkene.
Use curved arrows to show the two carbocations that can from from 1-methylcyclohexene.
3° carbocations are more stable than 2º carbocations, so only the 3º carbocation is formed.
Let's go over how a carbocation can form from an alcohol.
Write in the curved arrows to show the formation of the protonated alcohol, and water acting as a leaving group to form a carbocation.
Using curved hooks, draw a mechanism for the free radical bromination reaction shown below.
Note that the radical will form on the 3° carbon only, as this is the most stable radical.
Using curved arrows, draw a mechanism for the SN1 reaction shown below.