The law of detachment (or modus ponens, or affirming the antecedent) is a logical deduction of the following form:
You have a conditional statement `p->q` (p implies q or if p then q); then you are told that the hypothesis of the conditional (p) is true; then you can conclude that the conclusion of the conditional (q) is true.
For the given statements the conditional is: I will always go outside if the weather is nice. This can be put into the form `p->q` or if p then q: If the weather is nice, then I will go outside.
Then we are given the fact that it will be sunny (nice) on Tuesday. Thus the hypothesis is affirmed for Tuesday.
The answer is true. We can draw the conclusion that I will go outside on Tuesday.
Of course, you must be careful when transferring a logical argument from a conventional statement. It could be argued that sunny does not necessarily imply "nice" (as it could be sunny and -40 degrees outside.)