There are two main reasons why a tariff on Toyotas would lead to a decrease in the supply of that brand of car. To see what those reasons are, let us first look at what can cause supply to change. The supply of a given good can be changed by any one of six factors (or a combination of factors).
Supply will change if the number of sellers changes. The Toyota company is the only seller of Toyota cars (to dealers, that is). The tariff will not make Toyota fold, so the number of sellers will not change.
Supply will change if the technology used to make the good changes. This has nothing to do with tariffs.
Supply will change if the price of things that go into the good change. In other words, if the price of steel, which is used to make cars, rises, the supply of cars will decline. However, the tariff on Toyotas does not change the price of steel or any other input.
Supply will change if taxes or subsidies are imposed. A tax imposes an extra cost on the seller. If the seller’s costs rise, supply falls. If Toyota has to pay the tariff, the effective cost of making cars for sale in the US will rise. Toyota will be paying higher prices to make the cars and therefore it will not want to sell as many at any given price (this means any given price that it can charge customers). That is because it makes less profit at each price point. So, the fact that the tariff raises Toyota’s effect costs is one reason why a tariff will cause the supply of Toyotas to drop.
Supply can change if the price of other things the company could make changes. For example, if Toyota could choose to make tanks or cars and the price of tanks rises, Toyota might make fewer cars and more tanks. The tariff should not have an impact here.
Finally, supply can change as producers’ expectations change. If a producer does not think that a certain good will be profitable, they will not make as many of that good. In this case, the tariff will probably cause Toyota to conclude that they will not be able to make as much profit as they used to in the US. Therefore, they will stop making as many cars for the US market.
Thus, we can see that there are two reasons why a tariff on Toyota cars will make the supply of such cars go down: increased cost to the seller making the good more costly to produce and change in a producer's expectation of profit.