Does thyroxine increase BMR or metabolic rate?
The definition of BMR from wiki is :


  Basal metabolic rate (BMR) is the rate of energy expenditure per unit time by endothermic animals at rest.


When BMR is calculated for a volunteer some conditions are taken into account:


complete physical rest
sitting upright
at a comfortable room temperature usually around 25 centigrade
at the post-absorptive phase of digestion


On the other hand metabolic rate may be calculated even when one is exercising, at high or low room temperatures, during digestion etc. So it is more generalised.

When you are talking about thyroxine or thyroid hormones, you must keep in mind what (factors) stimulates its secretion.
One such factor is coldness.

So that definitely indicates temperatures below the 25 centigrade mark at which BMR is usually calculated.

So in my opinion it was quite prudent of your teacher to advise you to use metabolic rate instead of basal metabolic rate for the thyroxine effect description.

REFERENCE BOOK:
Biochemistry by Debajyoti Das 14 th edition
Academic publishers P-677 to 680.